MANAGEMENT ACCOUNTING ( In English ) Capital Budgeting

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 ###

Ex-01. 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%;

Ex-03. 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%.]

Ex-06. 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%.]

Ex-08. 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)

Ex-09. 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% ]

Ex-11. 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 :

[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

[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)

Ex-15. 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 ]

Ex-16. 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 ]

Ex-17. Dane Cosmetics is evaluating a new fragrance-mixing machine. The machine requires an initial investment of Tk 24.000 and will generate after-tax 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 (a-1) 2,675 (3) 7.19 Year, (b-1) 838 (2) 7.73 Year, (c-1) -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 (a-1) 2,58,200 (3) 3.29 Year, (b-1) 2,77,940 (2) 3.21 Year, (c-1) 1,54,860 (2) 3.82 Year ]

Ex-19. 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 ]

Ex-20. 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)

Ex-21. 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% ]

Ex-25. 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% ]

Ex-26. 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 ]

Ex-27. 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%]

Ex-28. 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% ]

Ex-29. 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
Yer	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% ]

Ex-30. 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%

Ex-31. 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% ]

Ex-33. 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 ]

Ex-34. 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 ###

Ex-01. 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 Co-efficient.

[Ans:- 1^st year =.0955; 2^nd year =.911; 3^rd year =.87; 4^th year = .8302; 5^th year = .7925

Ex-02. 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 Co-efficient.

[Ans:-

Ex-03. 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 =1-0.05t. Calculate the net present value of the Project if Risk free rate of return is 8%.

[Ans : NPV= 489 ]

Ex-04. 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 =1-0.05t. Calculate the net present value of the Project if Risk free rate of return is 7%.

[Ans : NPV= 1,016

Ex-05. You are supplied with the following information of XYZ Ltd.

Year	Project-1		Project-2
	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 :- Project-1. NPV= 98,431. Project-2. NPV= 65,095.

Comment : As the NPV of Project -1 is higher than that of Project -2. The company should select the Project-1

Ex-06. You are supplied with the following information of Rakibe Ltd.

Year	Project-1		Project-2
	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 Project-2.

Ex-07. Green Ltd. is Considering two mutually exclusive Project. The expected Cash flows of each Project are given below :

Year	Project-A	Certainty Equivalent	Praject-B	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.

Ex-08. A Co. is Considering two mutually exclusive Project. The expected Cash flows of each Project A & B.

Year	Project-A	Certainty Equivalent	Project-B	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 ###

Ex-01. 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 :

Project-X		Project-Y
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 Projects-X 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: Project-Y is more risky because there (C.V) is higher than Project-X.

Ex-02. 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 :

Project-M		Project-N
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]

Ex-03. Suppose there is a Project which involves initial cost of Tk 20,000 (cost at 1-0). It is expected to generate net cash flows during the first 2 years whith the Probability as Shown in the following table :

Year-1		Year-2
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) Year-1. NPV=10,000; Year-2. NPV=8,000. (2) Year-1. S.D=2,280; Year-2. S.D=2,280. (3) Year-1 & Year-2. NPV at 11%=(-4,498); (4) Year-1 & Year-2. S.D= 2,984]

Ex-04. Suppose there is a Project which involves initial cost of Tk 18,000 (cost at 1-0). It is expected to generate net cash flows during the first 2 years whith the Probability as Shown in the following table :

Year-1		Year-2
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:-

Ex-05. Your Company is Considering proposal for the parehase of a new machine on outlay of machine is given below (Tk 1,500 thousand )

Period-1		Period-2		Period-3
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; Period-2. S.D=90; Period-3. SD=261.53]

Ex-06. Your Company is Considering proposal for the parehase of a new machine on outlay of machine is given below (Tk 1,400 thousand )

Period-A		Period-B		Period-C
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 ###

Ex-01. 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)

Ex-02. 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)

Ex-03. 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).

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.

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