Question

You are considering the following two mutually exclusive projects. Both projects will be depreciated using straight-line depreciation to a zero book value over the life of the project. Neither project has any salvage value.

                 Project A   Project B
Year Cash Flow Year Cash Flow

0 -$45,000   0 $-40,000

1 $17,500 1 $8,200

2 $18,000   2 $ 14,600

3 $22,500 3 $ 36,800

Required Rate of Return

Project A- 8% Project B- 12%

Required Payback Period

Project A- 2 years Project B- 2 years

Required Accounting Return

Project A 8.5% Project B- 9.5%

a. (5 points) What is the NPV for each of the projects? Which project should be accepted if NPV method is applied? Explain why.

b. (5 points) What is the IRR for each of the projects? Which project should be accepted if IRR method is applied? Explain why.

c. (5 points) What is the payback period for each of the projects? Which project should be accepted if payback period method is applied? Explain why.

d. (5 points) What is the discounted payback period for each of the projects? Which project should be accepted if discounted payback period method is applied? Explain why.

e. (5 points) What is the profitability index for each of the projects? Which project should be accepted if profitability index method is applied? Explain why.

f. (5 points) What is the average accounting return (AAR) for each of the projects, assuming that cash flows occurring after year 0 are net income? Which project should be accepted if AAR method is applied? Also, assume that the target AAR is 10%.

g. (5 points) Define and find the crossover rate.

h. (5 points) Sketch the NPV profile. Plot all the relevant coordinates (i.e., the points on the x and y axis; and the cross-over rate) on the graph.

Answer 1

a) NPV = cash inflow/ (1+i)ⁿ - initial investment

where i = discount rate(i.e 8% for project A and 12% for project B)

n= periods (i.e 1,2,3,)

Depreciation for project A per year = 45000/3= 15000

Depreciation for project B per year = 40000/3= 13333(approx)

hence cash flows after depreciation for projects are :

project A : year 1: 17500+15000=32500, year 2 : 18000+15000=33000, year 3: 22500+15000=37500

similarly for project B : year 1=21533, year 2 =27933, year 3=50133

NPV for project A=32500(1+.08)+33000(1+.08)²+37500(1+.08)³ - 45000 =43153.5

similarly for project B NPV =37177.6

According to the NPV method Project A must be taken, because in NPV method the project with higher NPV is selected because it helps in increase in earnings for both the company and as well as the shareholders

b) IRR is the rate where NPV of the project is 0, if the IRR is higher than the required rate of return the project is profitable and if IRR< required rate of return project is rejected

The IRR formula is as follows:

hence substituting the values in the formula IRR for project A= 54.55% and IRR for project B =53%

hence according to IRR method Project A must be chosen as it is having higher IRR that project B and the iRR of project A exceeds required rate of return

c) Payback period is the time in which the firm is able to recover its initial outflow (i.e for project A=45000 and for project B =40000)

so payback period for project A= 1 year (32500 in 1 year) + .39 years(12500/33000) = 1.39 years

similarly for project B =1.66 years

hence project A must be taken as its payback period is less than project B .

d) Discounted payback period takes into account time value of money here the cash flows are taken after taking into time value of money and then payback method is applied.

For project A:

Particulars	Time Period	PV factor @ 8%	Amount	PV of amounnt
cash flow	1	.926	32500	30095
	2	.857	33000	28281
	3	.794	37500	29768.7

hence discounted payback period for project A = 1 year( 30095 in year 1)+.53 years (14905/28281) = 1.53 years

For Project B:

Particulars	Time Period	PV factor @ 12%	Amount	PV of amounnt
cash flow	1	.893	21533	19229
	2	.797	27933	22263
	3	.712	50133	35695

similarly discounted payback period of project B = 1year ( 19229 in year 1)+.93years (20771/22263)= 1.93 years

hence Project A must be taken as its discounted payback period is less than project B so it will recover money faster than project B and can have additional income.

e) Profitability Index(PI)=  present value of future cash flow / initial investment

Or = (NPV + Initial investment) ÷ Initial Investment

a firm must opt for a project whose PI is greater than or equal to 1

hence Profitability Index of Project A = (43153.5+45000)/45000=1.96

PI for project B = (37177.6+40000)/40000= 1.93

hence project A must be chosen as it has higher PI than project B and a higher PI indicates a more profitable project hence project A must be selected.