Question

Table Tools References Mailings Review View Help Design Layout Tell me Problem 3 Assume that you are the CFO at Porter Memorial Hospital The CEO has asked you to analyze two proposed capital investments: Project X and Project Y. Each project requires a net investment outay of $10,000, and the cost of capital for each project is 12 percent The projects expected net cash flows are as follows: Pr t Y Year Project X $10,000 $3,000 $1,000 $10,000 $3,000 $3,000 $3,000 $3,000 Calculate each project's payback period, net present value (NPV), and internal rate of return (IRR) a. b. Which project (or projects) is financially acceptable? Explain your answer

Answer 1

a.

Computation of payback periods:

	Project X		Project Y
Year	Cash flow	‘CUM Cash Flow	Cash flow	‘CUM Cash Flow
0	($10,000)	($10,000)	($10,000)	($10,000)
1	$6,500	($3,500)	$3,000	($7,000)
2	$3,000	($500)	$3,000	($4,000)
3	$3,000	$2,500	$3,000	($1,000)
4	$1,000	$3,500	$3,000	$2,000

Payback Period = A +B/C

Where,

A = Last period with a negative cumulative cash flow

B = Absolute value of cumulative cash flow at the end of the period A

C = Total cash flow during the period after A

Payback Period for Project X = 2 +│$ (500) │/$ 3,000

                            = 2 + $ 500/$ 3,000

                            = 2 + 0.166666667 = 2.166666667 or 2.17 years

Payback Period for Project Y = 3 +│$ (1,000) │/$ 3,000

                            = 3 + $ 1,000/$ 3,000

                            = 3 + 0.33333333 = 3.33333333 or 3.33 years

Payback Period of Project X is 2.17 years

Payback Period of Project Y is 3.33 years

Computation of NPV:

			Project X		Project Y
Year	Computation of PV factor	PV Factor @ 12 % (F)	Cash flow CX	PV (= CX x F)	Cash flow CY	PV (= CY x F)
0	1/(1+0.12)^0	1	($10,000)	($10,000)	($10,000)	($10,000)
1	1/(1+0.12)^1	0.8928571428571	$6,500	$5,803.5714	$3,000	$2,678.5714
2	1/(1+0.12)^2	0.7971938775510	$3,000	$2,391.5816	$3,000	$2,391.5816
3	1/(1+0.12)^3	0.7117802478134	$3,000	$2,135.3407	$3,000	$2,135.3407
4	1/(1+0.12)^4	0.6355180784048	$1,000	$635.5181	$3,000	$1,906.5542
			NPVX	$966.0119	NPVY	($887.9520)

NPV of Project X is $ 966.0119 or $ 966.01

NPV of Project Y is - $ 887.9520 or - $ 887.95

Computation of IRRs using excel:

	A	B	C
1	Year	Cash flow Project X	Cash flow Project Y
2	0	($10,000)	($10,000)
3	1	$6,500	$3,000
4	2	$3,000	$3,000
5	3	$3,000	$3,000
6	4	$1,000	$3,000
7	IRR	18.03%	7.71%

If excel sheet looks like above table,

To compute IRR for Project X insert formula “=IRR(B2:B6) in cell B7 to get IRR as 18.03 %

To compute IRR for Project Y insert formula “=IRR(C2:C6) in cell C7 to get IRR as 7.71 %

IRR of Project X is 18.03 %

IRR of Project Y is 7.71 %

Project X is financially acceptable as it has positive NPV and IRR is higher than required rate of return.

Project Y has negative NPV and its IRR is lower than firm’s required cost of capital. Hence it is not advisable to accept Project Y.

Also payback period of Project X is less than Project Y.