Question

Delta Dawn’s Bakery is considering purchasing a new van to deliver bread. The van will cost $18,000. Two-thirds ($12,000) of this cost will be borrowed. The loan is to be repaid with four equal annual payments (first payment at t = 1) based on an interest rate of 4%/year. It is anticipated that the van will be used for 6 years and then sold for a salvage value of $2,500. Annual operating and maintenance expenses for the van over the 6-year life are estimated to be $700 per year. If the van is purchased, Delta will realize a cost savings of $3,600 per year. Delta uses a MARR of 6%/year.

What is the present worth of the van?

Answer 1

Working notes:

(A) Loan repayment, years 1 to 4 = Loan amount / PVIFA(4%, 4) = 12,000 / 3.6299 = 3,305.88

(B) Annual net benefit (NB) ($) = Annual savings - Annual cost - Annual loan repayment

(C) NB in year 6 = Annual savings - Annual cost + $2,500 (Salvage value)

(D) First cost = $18,000 - $12,000 = $6,000

(E) PV Factor in year N = 1 / (1.06)^N

Therefore, Present Worth (PW) of NB is computed as follows.

Year	Savings ($)	Cost ($)	Loan Repaid ($)	NB ($)	PV factor @6%	Discounted NB ($)
	(1)	(2)	(3)	(4)=(1)-(2)-(3)	(5)	(4)x(5)
0		6,000		-6,000	1.0000	-6,000
1	3,600	700	3,305.88	-406	0.9434	-383
2	3,600	700	3,305.88	-406	0.8900	-361
3	3,600	700	3,305.88	-406	0.8396	-341
4	3,600	700	3,305.88	-406	0.7921	-321
5	3,600	700	0	2,900	0.7473	2,167
6	3,600	700	0	5,400	0.7050	3,807
					PW ($) =	-1,433