Question

1. Grand Vitamin Company is considering two investments, each of which costs $15,000. The cash flows are below.  

Compute the payback period for each.

Year	Project A	Project B
1	$22,000	$7,500
2	18,000	7,500
3	16,000	8,000

2. Which of the two projects in Problem 2 should be chosen based on the net present value method? Assume a cost of capital of 10 percent.  To earn credit, show both of your NPV answers.

3. The Tom Corp wants to know its cost of capital.  Its current capital structure calls for 45% debt, 15% preferred stock and 40% common equity.  Initially, common stock will be in the form of retained earnings.  The costs of the sources of financing are:  debt: 5.5%; preferred stock: 7.4%; retained earnings: 10%; and new common stock, 11.4%.  What is the weighted cost of capital?  Use 2 decimals

Answer 1

1. Payback period is the time taken by a project's cash inflows to recover its initial investment or cost.

Project A's payback period

initial cost of project is $15,000 which will be recovered by year 1's cash flow of $22,000. year 1 cash flow of $22,000 is higher than initial cost of $15,000. so, payback period will be less than 1.

payback period = $15,000/$22,000 = 0.68 years

Project B's payback period

initial cost of project is $15,000 which will be recovered by year 1's cash flow of $7,500 and remaining initial cost of $7,500 ($15,000 - $7,500) will be recovered by year 2's cash flow of $7,500. so, payback period is 2 years.

2. NPV is the difference between present value of cash inflows and initial investment or cost.

present value of cash inflows = Year 1 cash inflow/(1+cost of capital) + Year 2 cash inflow/(1+cost of capital)² + Year 3 cash inflow/(1+cost of capital)³

based on the net present value method, Project A should be chosen beause it has higher NPV of $31,897.07 than Project B's NPV of $4,027.05. higher positive NPV means higher profit.

Year	Project A	Project B
0	-$15,000	-$15,000
1	$22,000	$7,500
2	$18,000	$7,500
3	$16,000	$8,000
Cost of capital	10%	10%
NPV	$31,897.07	$4,027.05

Calculation

3. weighted cost of capital = weight of debt*cost of debt + weight of preferred stock*cost of preferred stock + weight of equity*cost of equity

cost of debt is the after-tax cost of debt. tax rate is not given in the question. so, it is assumed cost of debt of 5.5% is after-tax.

weighted cost of capital = 0.45*5.5% + 0.15*7.4% + 0.40*10% = 2.475% + 1.11% + 4% = 7.59%

the weighted cost of capital is 7.59%.