MANAGEMENT ACCOUNTING ( In English )
Capital Budgeting ( g~jab ev‡RwUs )
m~&&Î
 As‡Ki g‡a¨ hw` Tax Rate †`Iqv bv _v‡K Zvn‡j †h Amount ¸‡jv †`Iqv _vK‡e& J Amount †K CFAT / NCB a‡i AsK ïiæi Ki‡Z n‡e
 As‡Ki g‡a¨ hw` Tax Rate †`Iqv _v‡K, †Kvb ïiæi K_v D‡jøL bv _vwK‡j CFBT †_‡K AsKwU ïiæ Ki‡Z nB‡e Avi hw` †Kvb ïiæi K_v D‡jøL _v‡K Zvn‡j †mLvb †_‡K AsKwU ïiæ Ki‡Z nB‡e†hgb t Cash Flow BeforeTax = (CFBT), Earning Before Tax = (EBT),Earning After Tax = (EAT), Cash flow After Tax =(CFAT) / Net Cash Benefit = (NCB) BZ¨vw` _vK‡Z cv‡o
 CFBT – Dep: Exp = EBT – Tax Rate % = EAT + Dep : Exp = CFAT / NCB
 Dep : Exp =
1  2  3  4 = (2 – 3)  5 = (4 × Tr)  6 = (4 – 5)  7 = (6 + 3) 
Year  CFBT  Dep: Exp  EBT  Tax rate  EAT  CFAT/NCB 
(01). Pay Back Period (PBP) = wewb‡qvM cwi‡kvaKvj
(a) bM` cªev‡ni cwigvb mgvb n‡j t PBP = (b) bM` cªev‡nicwigvbAmgvbn‡j t PBP = A+ 
Here,
PBP = Pay Back Period = NCO = Net Cash Outlay = NCB = Net cash Benefit = Here, PBP = Pay Back Period. NCO = Net Cash Outlay = 
(02) Pay Back Reciprocal ( PBR) = cvi¯úvwiK wewb‡qvM cwi‡kvaKvj
(a) bM` cªev‡ni cwigvb mgvb n‡j t PBR = (b) bM` cªev‡ni cwigvb Amgvb n‡j t PBR = 
Here,
PBR = Pay Back Reciprocal NCB = Net cash Benefit = NCO = Net Cash Outlay = Here, PBR = Pay Back Reciprocal PBP = Pay Back Period. 
03. Surplus Life (SL)
SL = Use Life – PBP 
Here,
SL= Surplus Life = ? PBP = Pay Back Period = 
04. Surplus Cash Flow (SCF)
SCF = (Total Cash Flow /CFAT – NCO ) + S.V

SCF = Surplus Cash Flow = ?
NCO = Net Cash Outlay = S.V = Salvage Value = ? 
05. Index of Surplus Cash Flow (ISCF)
ISCF =

ISCF = Index of Surplus Cash Flow
SCF = Surplus Cash Flow = NCO = Net Cash Outlay = 
01. Average Rate of Return (ARR)= Mo DcvR©b nvi c×wZ
ARR =

Here,
ARR =Average Rate of Return Average EAT =
Average NCO = A_ev, As‡Ki g‡a¨ Working Capital _vK‡j, Average NCO = W.C+ 
02. Return on Investment (ROI)= Mo wewb‡qv‡Mi DcvR©b nvi
ROI = 
Here,
ROI = Return on Investment Average EAT =

03. Present Value Factor evwni Kivi m~G :
(a) bM` cªev‡ni cwigvb Amgvbn‡j t P/V Factor = (b) bM` cªev‡ni cwigvb Amgvbn‡j t P/V Factor = R


04. Net Present Value (NPV)
NPV = Total P/V – NCO 

05. Profitability Index (PI) = gybvdvi jf¨Zv m~PK PI = 
Here,
PI = Profitability Index. TPV = Total Present Value. NCO = Net Cash Outlay = 
06. Net Profitability Index (NPI)
NPI = PI – 100% 
Here,
NPI = Net Profitability Index PI = Profitability Index. 
07. Present value/ Discount (PBP)
(a) bM` cªev‡ni cwigvb mgvb n‡j t Present value/Discount (PBP) = (b) bM` cªev‡nicwigvbAmgvbn‡j t Present value/ Discount (PBP) = A+

Here,
Present value cash in flow = 
08. Internal Rate of Return ( IRR) = Af¨šÍixb gybvdvi nvi
IRR = A +

A = Lower Discount Rate = wb¤œ evUªvi ni
B = Higher Discount Rate = D”P evUªvi ni C = NPV of Lower Discount Rate = wb¤œ evUªvi nv‡ii bxU eZ©gvb g~j¨ D = NPV of Higher Discount Rate = D”P evUªvi nv‡ii bxU eZ©gvb g~j¨ 
3^{rd} Year
FINANCIAL MANAGEMENT
Chapter No (2)
Capital Budgeting and Risk Analysis
 ###Capital budgeting normal ###
Ex01. Rakib Company estimates that it can save Tk 40,000 a year in cash operating costs for next 5years. If it buy a machine at cost of Tk 1,50,000 No residual value is expected.
Required :
(1) Pay Back Period (PBP).
(2) Pay Back Reciprocal (PBR).
(3) Surplus life (SL).
(4) Surplus Cash Flow (SCF);
(5) Index of Surplus Cash Flow (ISCF)
[ Ans: (1) 3.75 years; (2) 26.67%; (3) 1.25 years; (4) Tk. 50,000; (5) 33.33%;
Exe 02. Compute the following information:
Net cash outlay = Tk. 1,00,000.
Yearly Net Cash Benefit = Tk. 30,000
Useful life = 5 years.
Required :
(1) Pay Back Period (PBP).
(2) Pay Back Reciprocal (PBR).
(3) Surplus life (SL).
(4) Surplus Cash Flow (SCF);
(5) Index of Surplus Cash Flow (ISCF)
[ Ans : (1) 3.33 years; (2) 30%; (3) 1.67 years; (4) Tk. 50,000; (5) 50%;
Ex03. SONY Company estimates that it can save Tk 25,000 per a year in cash operating costs for next 10 years. If it buy a machine at cost of Tk 1,10,000. No residual value is expected. Assume that income taxes rare overage 30% of taxable income. Compute the pay bank period.
Required :
(1) Pay Back Period (PBP).
(2) Pay Back Reciprocal (PBR).
(3) Surplus life (SL).
(4) Surplus Cash Flow (SCF);
(5) Index of Surplus Cash Flow (ISCF)
[ Ans: (1) 5.29 years. (2) 18.91%. (3) 4.71 years. (4) 98,000Tk. (5) 89.09%.
Exe 04. Compute the following information:
Net cash outlay = Tk. 1,00,000.
Yearly Net Cash Benefit = Tk. 30,000
Useful life = 5 years.
Tax rate = 25%
Required :
(1) Pay Back Period (PBP).
(2) Pay Back Reciprocal (PBR).
(5) Surplus life (SL).
(6) Surplus Cash Flow (SCF);
(7) Index of Surplus Cash Flow (ISCF)
[ Ans : (1) 3.64 years; (2) 28%; (3) 1.36 years; (4) Tk. 37,500; (5) 37.50% ]
Ex 05. A Company can Make either of two investment at the beginning of 2018. The details of the investment proposals are as given below :
NCO ———————————Tk.2,80,000
Life ———————————– 5 years
Scrap value ————————– NILL
Working capital ——————— NILL
Year  Net cash flow 
1  80,000 
2  80,000 
3  80,000 
4  80,000 
5  80,000 
Required :
(1) Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3) Surplus life (SL). (4) Surplus Cash Flow (SCF); (5) Index of Surplus Cash Flow (ISCF)
[Ans:(1) 3.5years.(2) 28.57%. (3) 1.50 years. (4) 1,20,000 Tk. (5) 42.86%.]
Ex06. There are two investment proposals. Following data are available about these proposals. ( Tk )
Investment ————————— 52,000
Expected life ————————— 6 year
Year  Cash in flower 
1  9,000 
2  9,000 
3  9,000 
4  9,000 
5  9,000 
6  9,000 
Required : Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3) Surplus life (SL). (4) Surplus Cash Flow (SCF); (5) Index of Surplus Cash Flow (ISCF)
[Ans: (1) 5.78years.(2) 17.31%. (3) .78 years. (4) 7,000 Tk. (5) 13.46%.]
Ex 07. A Company can Make either of two investment at the beginning of 2018. The details of the investment proposals are as given below :
NCO ————————————————— Tk. 2,00,000
Life —————————————————– 5 years
Scrap value ——————————————– NILL
Working capital ————————————— NILL
Year  Net cash flow 
1  50,000 
2  50,000 
3  60,000 
4  60,000 
5  60,000 
Required :
(1) Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3) Surplus life (SL). (4) Surplus Cash Flow (SCF); (5) Index of Surplus Cash Flow (ISCF)
[Ans: (1) 3.33years.(2) 27.32%. (3) 1.34 years. (4) 80,000 Tk. (5) 40%.]
Ex08. There are two investment proposals. Following data are available about these proposals. ( Tk )
Investment ———————— 80,000.
Expected life ———————— 5 year.
Year  Cash in flower 
1  10,000 
2  15,000 
3  20,000 
4  25,000 
5  30,000 
Required : (1) Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3) Surplus life (SL). (4) Surplus Cash Flow (SCF); (5) Index of Surplus Cash Flow (ISCF)
[Ans: (1) 4.33years.(2) 23.09%. (3) .67years. (4) 20,000 Tk. (5) 25%.]
Average Rate of Return / Return on Investment ( ARR/ROI)
Ex09. Rakib Ltd plans to buy a Bick which costs 1,00,000. The estimated Salvage value is Zero. Tax rate is 50%. The company uses straight line depreciation and proposed project has each year cash flows before tax as follows:
Year  Cash in flower 
1  30,000 
2  30,000 
3  30,000 
4  30,000 
5  30,000 
Required :
(1) Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3)Average Rate of Return (ARR) (4) Return On Investment (ROI) (5) Surplus life (SL). (6) Surplus Cash Flow (SCF); (7) Index of Surplus Cash Flow (ISCF)
[Ans : (1) 4 years. (2) 25%. (3) 10% (4) 5% (5) 1 years. (6) 25,000 (7)25% ]
Ex 10. MISESS Company Ltd plans to buy a machine which costs 2,00,000. The estimated Salvage value is Zero. Tax rate is 50%. The company uses straight line depreciation and proposed project has each year cash flows before tax as follows:
Year  CFBT 
1  60,000 
2  60,000 
3  60,000 
4  60,000 
5  60,000 
Required : (1) Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3)Average Rate of Return (ARR) (4) Return On Investment (ROI) (5) Surplus life (SL). (6) Surplus Cash Flow (SCF); (7) Index of Surplus Cash Flow (ISCF)
[Ans : (1) 4 years. (2) 25%. (3) 10% (4) 5% (5) 1 years. (6) 50,000 (7)25% ]
Ex11. Rakib Ltd plans to buy a Bick which costs 1,00,000. The estimated Salvage value is Zero. Tax rate is 50%. The company uses straight line depreciation and proposed project has each year cash flows before tax as follows:
Year  Cash in flower 
1  25,000 
2  30,000 
3  35,000 
4  40,000 
5  45,000 
Required :
(1) Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3)Average Rate of Return (ARR) (4) Return On Investment (ROI) (5) Surplus life (SL). (6) Surplus Cash Flow (SCF); (7) Index of Surplus Cash Flow (ISCF)
[Ans : (1) 3.83 years. (2) 26.11%. (3) 15% (4) 7.50% (5) 1.17 years. (6) 37,500 (7)37.50%
Ex 12. MISESS Company Ltd plans to buy a machine which costs 2,00,000. The estimated Salvage value is Zero. Tax rate is 50%. The company uses straight line depreciation and proposed project has each year cash flows before tax as follows:
Year  CFBT 
1  50,000 
2  60,000 
3  70,000 
4  75,000 
5  80,000 
Required : (1) Pay Back Period (PBP). (2) Pay Back Reciprocal (PBR). (3)Average Rate of Return (ARR) (4) Return On Investment (ROI) (5) Surplus life (SL). (6) Surplus Cash Flow (SCF); (7) Index of Surplus Cash Flow (ISCF)
[Ans : (1) 3.87 years. (2) 25.84%. (3) 13.50% (4) 6.75% (5) 1.13 years. (6) 67,500 (7)33.75% ]
Ex 13. Dina Enterprise is considering a new product line. The details of the investment proposal are follows :
Initial cash out lay Tk 1,00,000
Expected life 5 years
Scroll value 10,000
Working capital Tk 20,000
Year  Cash in flow (Tk) 
1  25,000 
2  30,000 
3  32,000 
4  35,000 
5  40,000 
The project cost of capital is 10% and tax rate 45%. Depreciation will be straight line basis. You are required to calculate :
(1) PBP. (2)PBR (3) ARR. (4) ROI.
[ Ans : 4.02 years. (2) 24.88% (3) 10.56% (4) 6.60%.]
Ex 14. Rakib Co. is considering a new product line. The details of the investment proposal are follows :
Initial cash out lay Tk 2,50,000
Expected life 5years
Scroll value 20,000
Working capital Tk 30,000
Year  Cash in flow (Tk) 
1  35,000 
2  50,000 
3  60,000 
4  70,000 
5  62,000 
The project cost of capital is 14% and tax rate 50%. Depreciation will be straight line basis. You are required to calculate (1) PBP. (2) ARR. (3) ROI.
[ Ans : 4.94 years. (2) 2.85%. (3) 1.69% ]
Net Present Value ( NPV)
Ex15. A firm whose cost of capital is 10% is considering two mutually exclusive projects cost Tk 70,000. Compute net present value.
Year  Cash inflow 
1  50,000 
2  40,000 
3  20,000 
4  10,000 
5  10,000 
Require :
 [Ans: 16,578 ]
 Discount (PBP) / Present value (PBP) [Ans : 76 years ]
Ex16. From the following information calculate net present value and comment on whether the project is Tk 50,000. Cost of capital is 12%.
Year  Amount (Tk) 
1  10,000 
2  7,000 
3  11,000 
4  6,000 
5  7,000 
Require :
 Discount (PBP) / Present value (PBP)
[ Ans : (i) NPV = (19,876). Comment : Since the NPV is negative , So the Project should not be accepted. (ii) 10 years ]
Ex17. Dane Cosmetics is evaluating a new fragrancemixing machine. The machine requires an initial investment of Tk 24.000 and will generate aftertax cash inflows of Tk 5,000 per year for 8 years. For each of the cost of capital listed, Assume that the firm has cost of capital is (a) 10%. (b) 12% and (c) 15%.
Calculate:
(1) Net present value (NPV).
(2) Present value (PBP)/Discount (PBP) .
[ Ans (a1) 2,675 (3) 7.19 Year, (b1) 838 (2) 7.73 Year, (c1) 805 (2) 8.28 Year ]
Ex 18. Initial cash outlay of a project Tk 5,00,000. Net cash benefit for the project Tk 2,00,000 per year. Cost of capital (a)10% ; (b) 9% and (b)16% expected life 5 years. Calculate:
(1)Net present value (NPV).
(2) Present value (PBP)/ Discount (PBP).
[ Ans (a1) 2,58,200 (3) 3.29 Year, (b1) 2,77,940 (2) 3.21 Year, (c1) 1,54,860 (2) 3.82 Year ]
Ex19. Jamun Ltd. Is considering the purchase of a machine costing Tk 1,50,000. The salvage value of the machine after 5 years will be Tk 30,000. The cash inflows will be as follows : 1^{st} year Tk 50,000; 2^{nd} year Tk 65,000; 3^{rd} year Tk 80,000; 4^{th} year Tk 40,000; 5^{th} year Tk 30,000. Assume the cost of capital is 15% ,should the company buy the machine ?
Calculate:
(1)Net present value (NPV). [ Ans : 47,927 ]
(2) Present value (PBP) /Discount (PBP). [ Ans : 3.21 year ]
Ex20. Suppose you have a plant purchase of a machine costing Tk 1,50,000. The salvage value of the machine after 5 years will be Tk 40,000. The cash inflows will be as follows : 1^{st} year Tk 50,000; 2^{nd} year Tk 55,000; 3^{rd} year Tk 70,000; 4^{th} year Tk 30,000; 5^{th} year Tk 20,000. Assume the cost of capital is 14% ,should the company buy the machine ?
Calculate :
(1)Net present value (NPV). [ Ans : 32,351]
(2) Present value (PBP)/ Discount (PBP). [Ans : 3.93 year ]
Internal rate of return (IRR)
Ex21. A Company is considering the purchase of a machine. The cost of machine is Tk 5,00,000. In comparing the profitability of machines a discount rate of 15% is to be used.
Year  Cash flows (Tk) 
1  1,00,000 
2  1,20,000 
3  1,50,000 
4  1,90,000 
5  2,50,000 
Required :
(1) NPV. [ Ans : 9,950 ]
(2) Internal Rate of Return (IRR). [ Ans : 15.67% ]
(3) Present Value PBP. [ Ans : 4.92 years ]
Ex 22. A Company is considering the purchase of a machine. The cost of machine is Tk 1,00,000. In comparing the profitability of machines a discount rate of 12.50% is to be used. Earning after taxation EAT are expected to be as follows.
Year  Cash flows (Tk) 
1  15,000 
2  20,000 
3  25,000 
4  15,000 
5  10,000 
Required :
(1) NPV. [ Ans : 32,819 ]
(2) Internal Rate of Return (IRR). [Ans : 26.37% ]
(3) Present Value PBP. [ Ans : 3.26 ss years ]
Ex 23. Suppose you have a plant purchase of a machine costing Tk 1,00,000. The salvage value of the machine after 5 years will be Tk 10,000. The cash inflows 25,000 per year. Assume a required rate of return of 15% and a 30% tax rate. The company has a policy of charging depreciation of straight line method.
Required :
(1) Pay Back Period (PBP). [ Ans : 4.36 year ]
(2) Net present value (NPV). [ Ans : (18,263) ]
(3) Internal Rate of Return (IRR). [ Ans : 7.77% ]
Ex 24. Mr Rakib Co.purchase of a machine costing Tk 3,00,000. The salvage value of the machine after 10 years will be Tk 30,000. The cash inflows 70,000per year. Assume a required rate of return of 14% and a 25% tax rate. The company has a policy of charging depreciation of straight line method.
Required :
(1) Pay Back Period (PBP). [ Ans : 5.06 year ]
(2) Net present value (NPV). [ Ans : 17,146 ]
(3) Internal Rate of Return (IRR). [ Ans : 15.43% ]
Ex25. Rakib Company estimates that it can save Tk 40,000 a year in cash operating costs 2,50,000 for next 10 years. The salvage value of Tk 50,000 per year. Cost of capital is 10% .
Compute :
(1) Pay Back Period (PBP). [ Ans : 6.25 year ]
(2)Average Rate of Return (ARR) [ Ans : 13.33% ]
(3) Return On Investment (ROI) [ Ans : 8% ]
(4) NPV. [ Ans: 15,059 ]
(5) IRR. [ Ans : 11.40% ]
Ex26. Fresh Departmental store can build a new sign for Tk 50,000 which will increase its expected net cash flows by Tk 5,000 per year for the next 20 years by attracting additional customers. The sign has a zero expected salvage value , Rahul’s cost of capital is 10% Compute :
(1) NPV. [ Ans : 7,432 ]
(2) IRR. [ Ans : 8.36% ]
(3) Pay Back Period (PBP). [ Ans : 10 year ]
Ex27. A Company want to invest in a project the initial outlay of which is Tk 50,000. The relevant cash flows of the project is given below
Yer  Cash flows 
1  12,000 
2  12,000 
3  12,000 
4  12,000 
5  12,000 
The firm cost of capital is 14% calculate :
(1) Payback period (PBP).
(2) Pay Back Reciprocal (PBR).
(3) Average rate of return (ARR).
(4) Return on Investment (ROI).
(5) Net present value (NPV).
(6) Internal Rate of Return (IRR).
(7) Present value (PBP)
(8) Profitability index (PI).
(9) Net profitability index (NPI)
[Ans: (1) 4.17 year (2) 24% (3) 8% (4) 4% (5) 8,803 (6) 6.47% (7) 6.07 year (8) 82.39% (9) 17.61%]
Ex28. A company wants to invest in a project the initial outlay of which is Tk 25,000. The relevant cash flows of the project is given below :
Year  Cash flows 
1  9,000 
2  9,000 
3  9,000 
4  9,000 
5  9,000 
The firms cost of capital is 14% calculate :
(1) Payback period (PBP).
(2) Pay Back Reciprocal (PBR).
(3) Average rate of return (ARR).
(4) Return on Investment (ROI).
(5) Net present value (NPV).
(6) Internal Rate of Return (IRR).
(7) Present value (PBP)
(8) Profitability index (PI).
(9) Net profitability index (NPI).
[Ans: (1) 2.78 year (2) 36% (3)3.20% (4) 3.20% (5) 5,898 (6) 23.85% (7) 4.05 year
(8) 123.59 (9) 23.59% ]
Ex29. A Company want to invest in a project the initial outlay of which is Tk 50,000. The relevant cash flows of the project is given below
Yer  Proposal – B 
Cash flows  
1  20,000 
2  15,000 
3  10,000 
4  20,000 
The firm cost of capital is 14% calculate :
(1) Payback period (PBP).
(2) Pay Back Reciprocal (PBR).
(3) Average rate of return (ARR).
(4) Return on Investment (ROI).
(5) Net present value (NPV).
(6) Internal Rate of Return (IRR).
(7) Present value (PBP)
(8) Profitability index (PI).
(9) Net profitability index (NPI).
[Ans: (1) 2.78 year (2) 36% (3)3.20% (4) 3.20% (5) 5,898 (6) 23.85% (7) 3.95 yeae. (8) 95.36% (9) 4.64% ]
Ex30. A company wants to invest in a project the initial outlay of which is Tk 25,000. The relevant cash flows of the project is given below :
Year  Cash flows 
1  12,000 
2  10,000 
3  7,000 
4  8,000 
5  6,000 
The firms cost of capital is 14% calculate :
(1) Payback period (PBP). (2) Pay Back Reciprocal (PBR). (3) Average rate of return (ARR). (4) Return on Investment (ROI). (5) Net present value (NPV).
(6) Internal Rate of Return (IRR). (7) Profitability index (PI). (8) Net profitability index (NPI).
[Ans: (1) 2.43 year (2) 41.15% (3)28.80% (4) 14.40% (5) 5,799 (6) 24.85% (7) 123.20 yeae. (8) 23.20%
Ex31. A Rasor company is considering a project which requires an investment of Tk 4,50,000. The estimated salvage value is zero. Tax rate is 50%. The company uses straight line depreciation and the proposed project has cash flows before tax (CFBT) as follows :
Yeat  CFBT 
1  1,20,000 
2  1,00,000 
3  1,50,000 
4  1,30,000 
5  2,10,000 
Determine the following :
(1) Payback period (PBP (2) Average rate of return (ARR). (3) Internal Rate of Return (IRR). (5) Net present value @ 15% PV factor.
[Ans: (1) 4.13 year (2) 11.55% (3) 8.63% (4) (70,400)
Ex 32. A Rasor company is considering a project which requires an investment of Tk 2,25,000. The estimated salvage value is zero. Tax rate is 50%. The company uses straight line depreciation and the proposed project has cash flows before tax (CFBT) as follows :
Yeat  CFBT 
1  60,000 
2  50,000 
3  75,000 
4  65,000 
5  1,05,000 
Determine the following :
(1) Payback period (PBP
(2) Average rate of return (ARR).
(3)Net present value @ 15% PV factor.
(5) Internal Rate of Return (IRR).
[Ans: (1) 4.13 year (2) 11.55% (3) 35,245 (4) 8.76% ]
Ex33. A Company is considering an invest proposal which requires an initial cash outlay of Tk 50,000. The investment will have a life of 5 year. The project will have no salvage value at the end of the life. The company uses straight line method of depreciation. The company’s tax rate is 35%. The estimated cash flows before tax are as follows :
Year  Cash flows 
1  12,000 
2  14,000 
3  16,000 
4  18,000 
5  20,000 
The PV factors are : .89286; .79719; .71178; .63552; .56743
Required :
(1) PBP; (2) NPV; (3) PI; (4) NPI; (5) S.L
[Ans: (1) 4.80 year; (2) 949 (3) 0.98.11% (4) 1.90% (5) 1.20 year ]
Ex34. A Company is considering an invest proposal which requires an initial cash outlay of Tk 70,000. The investment will have a life of 5 year. The project will have no salvage value at the end of the life. The company uses straight line method of depreciation. The company’s tax rate is 40%. The estimated cash flows before tax are as follows :
Year  Cash flows 
1  18,000 
2  14,000 
3  25,000 
4  18,000 
5  20,000 
The PV factors are : 0.9091; 0.8264; 0.7513; 0.6830; and 0.6209.
Required : (1) PBP; (2) NPV; (3) PI; (4) NPI; (5) S.L
[Ans: (1) 4.15 year; (2) 5,915; (3) 92.74% (4) 7.26% (5) 0.85 year ]
Ex 35. Bloom Enterprise is considering a new product line. Th details of the investment proposal are follows :
Initial cash out lay Tk 1,20,000
Expected life 5 year
Scrap value Tk 10,000
Working capital Tk 20,000
Year  Cash inflow (Tk) 
1  28,000 
2  30,000 
3  37,000 
4  35,000 
5  40,000 
The project cost of capital is 10% and tax rate 45%. Depreciation will be on straight line basis. You are required to calculate :
(1) Payback period (PBP); (2) Return on Investment (ROI); (3) Average rate of return (ARR); (4)Net present value( NPV). (5) Internal Rate of Return (IRR); (6) Profitability index (PI)
(7) Net profitability index (NPI).
[Ans : (1) 4.90; (2) 4.71%; (3) 7.76%; (4) 14,115; (5) 6.60%; (6) 90%. (7) 10% ]
Ex 36. Bloom Enterprise is considering a new product line. Th details of the investment proposal are follows :
Initial cash out lay Tk 1,00,000
Expected life 5 year
Scrap value Tk 10,000
Working capital Tk 20,000
Year  Cash inflow (Tk) 
1  25,000 
2  30,000 
3  32,000 
4  35,000 
5  40,000 
The project cost of capital is 12% and tax rate 40%. Depreciation will be on straight line basis. You are required to calculate :
(1) Payback period (PBP); (2) Return on Investment (ROI); (3) Average rate of return (ARR); (4) Net present value( NPV). (5) Internal Rate of Return (IRR); (6) Profitability index (PI) (7) Net profitability index (NPI).
[Ans : (1) 3.93; (2) 7.20%; (3) 11.52%; (4) 5,669; (5) 9.89%; (6) 78.61%.
(7) 21.39% ]
 ### Certainty equivalent ###
Ex01. Assume risk free rate of return is 5% and risk adjusted discount rate ( RADR) is 10% and time period is 5 years. You are required to calculate certainty equivalent Coefficient.
[Ans: 1^{st} year =.0955; 2^{nd} year =.911; 3^{rd} year =.87; 4^{th} year = .8302; 5^{th} year = .7925
Ex02. Assume risk free rate of return is 7% and risk adjusted discount rate ( RADR) is 14% and time period is 5 years. You are required to calculate certainty equivalent Coefficient.
[Ans:
Ex03. The expected Cash flows of a Project are as follows :
Year  Cash flow (Tk) 
0  (28,000) 
1  6,000 
2  7,000 
3  10,000 
4  11,000 
5  9,000 
The certainty equivalent factor behaves as per the following equation : a =10.05t. Calculate the net present value of the Project if Risk free rate of return is 8%.
[Ans : NPV= 489 ]
Ex04. The expected Cash flows of a Project are as follows :
Year  Cash flow (Tk) 
0  (20,000) 
1  5,000 
2  6,000 
3  4,000 
4  7,000 
5  9,000 
The certainty equivalent factor behaves as per the following equation : a =10.05t. Calculate the net present value of the Project if Risk free rate of return is 7%.
[Ans : NPV= 1,016
Ex05. You are supplied with the following information of XYZ Ltd.
Year  Project1  Project2  
Cash flow (Tk)  Certainty equivalent  Cash flow (Tk)  Certainty equivalent  
0  (5,00,000)  1.00  (6,00,000)  1.00 
1  2,50,000  .95  3,50,000  .90 
2  3,00,000  .85  2,50,000  .80 
3  2,00,000  .70  2,50,000  .70 
4  1,50,000  .65  2,00,000  .60 
Which project should be accepted to the company. If the risk free discount rate is 10%.
[Ans : Project1. NPV= 98,431. Project2. NPV= 65,095.
Comment : As the NPV of Project 1 is higher than that of Project 2. The company should select the Project1
Ex06. You are supplied with the following information of Rakibe Ltd.
Year  Project1  Project2  
Cash flow (Tk)  Certainty equivalent  Cash flow (Tk)  Certainty equivalent  
0  (4,00,000)  1.00  (3,50,000)  1.00 
1  1,50,000  .95  2,50,000  .90 
2  2,00,000  .85  1,50,000  .80 
3  2,50,000  .70  1,00,000  .70 
4  1,00,000  .65  2,00,000  .60 
Which project should be accepted to the company. If the risk free discount rate is 12%.
[Ans:
Comment : As the NPV of Project 2 is higher than that of Project 1.The company should select the Project2.
Ex07. Green Ltd. is Considering two mutually exclusive Project. The expected Cash flows of each Project are given below :
Year  ProjectA  Certainty Equivalent  PrajectB  Certainty Equivalent 
0  (3,00,000)  1.00  (3,00,000)  1.00 
1  1,00,000  .95  2,00,000  .90 
2  2,00,000  .90  2,00,000  .80 
3  2,00,000  .85  2,00,000  .70 
4  3,00,000  .80  3,00,000  .60 
5  3,00,000  .75  4,00,000  .50 
The Company has decided to evaluate these Project using Certainty equivalent Method. Company’s normal required rate of return is 15% and after tax risk free rate of return is 8%. Which Project should be selected ?
[Ans: Project(A). NPV= 4,06,773; Project(B). NPV=3,83,400 ]
Comment : Which NPV of Project(A) should be select because hirethen.
Ex08. A Co. is Considering two mutually exclusive Project. The expected Cash flows of each Project A & B.
Year  ProjectA  Certainty Equivalent  ProjectB  Certainty Equivalent 
0  (4,00,000)  1.00  (2,00,000)  1.00 
1  1,00,000  .95  1,50,000  .90 
2  1,50,000  .90  2,00,000  .80 
3  2,00,000  .85  2,50,000  .70 
4  3,00,000  .80  1,0,00,000  .60 
5  3,50,000  .75  3,00,000  .50 
The Company has decided to evaluate these Project using Certainty equivalent Method. Company’s normal required rate of return is 13% and after tax risk free rate of return is 7%. Which Project should be selected ?[Ans: (A) 1,15,724 (B) 2,75,324)
Comment : Which NPV of Project(B) should be select because hight.
 ### Probability Distribution ###
Ex01. ABC Company Ltd is considering two mutually exclusive Project X and Y. Project X costs Tk 3,00,000 and Project Y Tk 3,00,000. You have been supplied with following NPV and Probability distribution for each Project :
ProjectX  ProjectY  
Estimated NPV  Probability  Estimated NPV  Probability 
30,000  .10  30,000  .20 
60,000  .40  60,000  .30 
1,20,000  .40  1,20,000  .30 
1,15,000  .10  1,50,000  .20 
Required :
(1) Compute the expected NPV of ProjectsX and Y.
(2) Compute the risk attached to each Project that is Standard Deviation of each
Probability distribution.
(3) Which Project do you consider more risky and why ?
[Ans:(1)Project (X) NPV=90,000; Project (Y).NPV= 70,000. (2) Project (X) S.D = 37,947; Project(Y).NPV = 44,497. (3) Project(X) C.V=.422; Project(Y) C.V=.494]
Comment: ProjectY is more risky because there (C.V) is higher than ProjectX.
Ex02. A Company is Considering two mutually exclusive Project M and N. Project –M costs Tk 5,00,000 and Project N Tk 5,60,000. You have been supplied with following NPV and Probability distribution for each Project :
ProjectM  ProjectN  
Estimated NPV  Probability  Estimated NPV  Probability 
40,000  .10  40,000  .20 
50,000  .50  50,000  .40 
1,00,000  .30  1,00,000  .30 
1,20,000  .10  1,20,000  .10 
Required:
(1) Compute the expected NPV of Project M and N.
(2) Compute the risk attached to each Project, that is Standard Deciation of each
probability distribution.
(3) Which Project do you consided more risk and why ?
[Ans: (1) Project (M) NPV=71,000; Project (N).NPV= 70,000. (2) Project (M) S.D = 28,443; Project(N).S.D= 29,326. (3) Project(M) C.V=.40; Project(N) C.V=.42]
Ex03. Suppose there is a Project which involves initial cost of Tk 20,000 (cost at 10). It is expected to generate net cash flows during the first 2 years whith the Probability as Shown in the following table :
Year1  Year2  
Probability  Net cash flow  Probability  Net cash flow 
.10  6,000  .10  4,000 
.25  8,000  .25  6,000 
.30  10,000  .30  8,000 
.25  12,000  .25  10,000 
.10  14,000  .10  12,000 
Required:
(1) Calculate expected value of Net cash flows for different periods.
(2) Calculate the Standard Deviation of Possible net cash flows for different periods.
(3) Calculate NPV if discount rate is 11%.
(4) Calculate the Standard Deviation of NPV.
[Ans: (1) Year1. NPV=10,000; Year2. NPV=8,000. (2) Year1. S.D=2,280; Year2. S.D=2,280. (3) Year1 & Year2. NPV at 11%=(4,498); (4) Year1 & Year2. S.D= 2,984]
Ex04. Suppose there is a Project which involves initial cost of Tk 18,000 (cost at 10). It is expected to generate net cash flows during the first 2 years whith the Probability as Shown in the following table :
Year1  Year2  
Probability  Net cash flow  Probability  Net cash flow 
.10  4,000  .10  1,000 
.25  6,000  .25  5,000 
.30  8,000  .30  7,000 
.25  10,000  .25  9,000 
.10  12,000  .10  11,000 
Required:
(1) Calculate expected value of Net cash flows for different periods.
(2) Calculate the Standard Deviation of Possible net cash flows for different periods.
(3) Calculate NPV if discount rate is 10%.
(4) Calculate the Standard Deviation of NPV.
[Ans:
Ex05. Your Company is Considering proposal for the parehase of a new machine on outlay of machine is given below (Tk 1,500 thousand )
Period1  Period2  Period3  
CFAT  Probability(P)  CFAT  Probability(P)  CFAT  Probability 
800  .1  800  .1  1,200  .2 
600  .2  700  .3  900  .5 
400  .4  600  .4  600  .2 
200  .3  500  .2  300  .1 
The probability distribution is assumed to independent. Risk free rate of interest is 15%. Calculate
(1) Expected NPV of project (2) The S.D of the Probability distribution of NPV:
[Ans: NPV=197; (2) Period (1) S.D=188.68; Period2. S.D=90; Period3. SD=261.53]
Ex06. Your Company is Considering proposal for the parehase of a new machine on outlay of machine is given below (Tk 1,400 thousand )
PeriodA  PeriodB  PeriodC  
CFAT  Probability(P)  CFAT  Probability(P)  CFAT  Probability 
750  .1  600  .1  900  .2 
500  .2  700  .3  800  .5 
300  .4  500  .4  750  .2 
400  .3  300  .2  500  .1 
The probability distribution is assumed to independent. Risk free rate of interest is 12%. Calculate the:
(1) Expected NPV of project (2) The S.D of the Probability distribution of NPV:
[Ans:
04 ### Decision Tree ###
Ex01. A compay is considing the purchases of a new equipment. The ned cash flows of the equipment have been estimated as given balow. The equipment hife is estimated to be twe yeas.
Initial probability CFAT  Conditional probability CFAT 
0.50 800
Tk 10,000 0 .40 0.50 12,000
0.40 16,000 Tk 12,000 0.60 0.20 20,000 
The cost of equipment is Tk 20,000 and the Company’s cost of capital is 12%.
Required:
 What are the joint probabilities of occurrence ?
 If the risk free rate is 12 what is
(a)The NPV of each of the vrances.
(b) The expected value (NPV)
(c) To recommend whether the equipment should be bough or not.
Ex02. A company is conceding the purchases of a new equipment. The ned cash flows of the equipment have been estimated as given below. The equipment hife is estimated to be twe yeas.
Initial probability CFAT  Conditional probability CFAT 
0.40 700
Tk 9,000 0 .35 0.50 10,000
0.30 15,000 Tk 11,000 0.50 0.15 28,000 
The cost of equipment is Tk 20,000 and the Company’s cost of capital is 12%.
Required:
 What are the joint probabilities of occurrence ?
 If the risk free rate is 12 what is
(a)The NPV of each of the vrances.
(b) The expected value (NPV)
(c) To recommend whether the equipment should be bough or not.
Ex03. PQR Company wants to purchase a new machine costing Tk 30,000 that has an expected life of 2 year. The probability distribution of CFAT are as follows :
.
Year – 1  Year – 2 
Initial probability CFAT  Conditional probability CFAT 
.30 10,000
0.4 Tk 15,000.4010,500 .3020,000 30,000 .4020,000 0.6 Tk 25,000 .4025,000 .2030,000 
(1)What are the joint probabilities of occurrence ?
(2)If the risk free rate is 10% what is.
(a)The NPV of each of the branches.
(b)The expected values (NPV).
(c) SD of probability distribution of NPV’s.
Ex 04. Priti Company wants to purchase a new machine costing Tk 5,000 that has an expected life of 2 years. The probability distribution of CFAT are as follows :
Year – 1  Year – 2 
Initial probability CFAT  Conditional probability CFAT 
0.3 2,000
0.4 Tk 2,500 0.4 2,500 0.3 3,000
0.4 3,000 0.6 Tk 3,500 0.4 3,500 0.2 4,500 
 What are the joint probabilities of occurrence ?
 If the risk free rate is 10% what is –
(a) The NPV of each of the branches
(b) The expected values (NPV)
(c) SD of the provability distribution of NPS ‘s.
 ### CAPM (Capital Assets Pricing Model ) ###
Calculate the expected rate of return for security A form the followings :
Rf = 10%, Rm = 18%, A = 1.35.