Question

Laura wants to buy a delivery truck. The truck costs $132,000 , and will allow her to increase her after tax profits by $24,000 per year for the next 10 years. She will borrow 80% of the cost of the truck for 10 years, at an interest rate of 6%. Laura’s unlevered cost of capital is 17% and her tax rate is 34%. The loan includes a $1,000 application fee. What is the NPV of buying the truck on these terms?

Answer 1

a) Cash outflow at the beginning = Cost of the machine - (loan received - application fee)= 1,32,000-(1,32,000*80% - 1,000) = 27400

b) Cash flow for 10 years = present value of increase in revenue for 10years less loan repayment

=118985- 14347.63*PVAF(10yrs,17%) = 118985-66840 = 52145

c) NPV = b-a = 52145-27400 = $24745

Working note 1: Calculation of Present value of revenue

year	Revenue	Tax savings on interest	Revenue-tax savings	PVF@17%	PV
1	24000	6336*34%=2154	26154.24	0.8547	22354
2	24000	5855*34%=1991	25990.7	0.7305	18986
3	24000	5346*34%=1817	25817.64	0.6243	16118
4	24000	4806*34%=1634	25634.04	0.5336	13678
5	24000	4233*34%=1439	25439.22	0.4561	11603
6	24000	3626*34%=1232=	25232.84	0.3898	9836
7	24000	2983*34%=1014	25014.22	0.3331	8332
8	24000	2301*34%=782	24782.34	0.2847	7056
9	24000	1578*34%=537	24536.52	0.2434	5972
10	24000	872.3*34%=276	24276.18	0.208	5049

present value of Total revenue = $118985

Working note 2 : Repayment schedule of loan

Given

amount of loan = $1,32,000*80% = 1,05,600

rate of interest = 6%

no. of years = 10 years

Cumulative discount factor = 7.3601

Yearly repayment amount = $1,05,600/7.3601 = 14,347.63

year	EMI	Principal at beginning	Interest @6%	Principal
1	14,347.63	105600	6336	8011.63
2	14,347.63	97,588.37	5855	8492.63
3	14347.63	89095.74	5346	9001.63
4	14347.63	80094.11	4806	9541.63
5	14347.63	70552.48	4233	10114.63
6	14347.63	60437.85	3626	10721.63
7	14347.63	49716.22	2983	11364.63
8	14347.63	38351.59	2301	12046.63
9	14347.63	26304.96	1578	12769.63
10	14347.63	13535.33	812.3	13535.63