Question

Laura wants to buy a delivery truck. The truck costs $114,000 , and will allow her to increase her after tax profits by $17,000 per year for the next 10 years. She will borrow 99% of the cost of the truck for 10 years, at an interest rate of 6%. Laura’s unlevered cost of capital is 15% and her tax rate is 22%. The loan includes a $2,000 application fee. What is the NPV of buying the truck on these terms?

Answer 1

Cost of the truck (V) = $114000

Debt (D) = $112860

Equity (E) = $1140

Interest on debt (Rd) = 6%

Unlevered cost (Re) = 15%

tax rate (TR) = 22%

Levered cost of capital (WACC) = (E/V​×Re)+(D/V×Rd×(1−TR))

= 4.78%

Profit for every year = $17000

we will subtract interest from every year and then calculate the present value of every year

Formula for present value = FV/(1+r)^n

​where:

FV=Future Value

r=Rate of return

n=Number of periods​

Particulars	1	2	3	4	5	6	7	8	9	10
Profit	17000	17000	17000	17000	17000	17000	17000	17000	17000	17000
Application fee	2000
Truck loan	6771.6	6771.6	6771.6	6771.6	6771.6	6771.6	6771.6	6771.6	6771.6	119632
CF	8228.4	10228.4	10228.4	10228.4	10228.4	10228.4	10228.4	10228.4	10228.4	-102631.6
PV	7852.79	9315.89	8890.63	8484.79	8097.47	7727.83	7375.07	7038.41	6717.12	-64322.74
NPV	7177.26

For NPV we just add all the PV's and we will get the result

which here is == NPV = $ 7177.26