Question

Worldwide trousers is considering an expansion of their existing business. The incremental after-tax cash flows to the project are:

Year 0: $-25,500

Year 1: $5,500

Year 2: $7,500

Year 3: $8,500

Year 4: $10,000

The unlettered cost of equity is 10%. The corporate tax rate is 40%.

A. Calculate the NPV of the project if it is all equity financed.

B. Worldwide plans to issue a 4-year loan for $12,000 at an interest rate of 8% to partially finance the project. All principal will be repaid in one lump-sum at the end of the fourth year. Calculate the adjusted present value of the investment project.

Answer 1

A) NPV = Present value (P. V) of cash flow - Investment cost

Here, i (Cost of equity) = 10% or 0.10

n = years

Years	Cash flow	P. V. Factor (1/(1+i)^n)	P. V. Of cash flow (Cash flow * P. V. Factor)
1	$5,500	(1/(1+0.10)^1) = 0.9091	$5,000.05
2	$7,500	(1/(1+0.10)^2) = 0.8265	$6,198.75
3	$8,500	(1/(1+0.10)^3) = 0.7513	$6,386.05
4	$10,000	(1/(1+0.10)^4) = 0.6830	$6,830
		Total	$24,414.85

NPV = $24,414.85 - $25,500 = (- $ 1,085.15)

B) P. V. Of debt financing = (Debt * Rate * Tax rate) * ((1 - (1/(1+i)^n))/i)

Here,

i (interest rate) = 8% or 0.08

n (years) = 4

Tax rate = 40% or 0.40

Now,

P. V. Of debt financing = ($12,000 * 8% * 0.40) * ((1 - ((1/(1+0.08)^4))/0.08)

P. V. Of debt financing = $384 * ((1 - 0.7350)/0.08)

P. V. Of debt financing = $384 * 3.3125

P. V. Of debt financing = $1,272

Adjusted present value = NPV + P. V. Of debt financing

Adjusted present value = (- $1,085.15) + $1,272

Adjusted present value = $186.85