Question

A car dealer leases a small computer with software for $5,000 per year. As an alterative he could buy the computer for $7,500 and lease the software for $3,500 per year. Any time he would decide to switch to some other computer he could cancel software lease and sell the computer for $500.  

A. If he buys the computer and leases the software, what is the payback period?

B. If he kept the computer and software for 8 years, what would be the benefit-cost ratio, based on a 5% interest rate.

Answer 1

Answer :-

given :-

A car dealer leases a small computer with software for = $5,000 per year.

an alterative he could buy the computer for = $7,500

lease the software for = $3,500 per year.

(A):-

Payback period = 2 + ( $7500 - $7000)/$3500

= 2+500/3500

= 2+1/7

= 2+ 0.14

= 2.14 years

payback period = 2.14 years

Years	cash outflows	cash inflows	cumulative Cash flows
0	$7500
1	$0	$3500	$3500
2	$0	$3500	$7000
3	$0	$3500	$10,500
4	$0	$3500	$14,000

(B):-

Benefit - cost ratio = present value of benefits /present value of costs

Present value of benefits = 3500/(1 + 5%)^1+ 3500/(1 + 5%)^2 + 3500/(1 + 5%)^3 + 3500/(1+5%)^4 + 3500/(1 + 5%)^5 + 3500/(1 + 5%)^6 + 3500/(1+ 5%)^7 + 3500/(1+ 5%)^8

= 3500/(1 + 0.05)^1+ 3500/(1 + 0.05)^2 + 3500/(1 + 0.05)^3 + 3500/(1+0.05)^4 + 3500/(1 + 0.05)^5 + 3500/(1 + 0.05)^6 + 3500/(1+ 0.05)^7 + 3500/(1+ 0.05)^8

= 3500/(1.05)^1+ 3500/(1.05)^2 + 3500/(1.05)^3 + 3500/(1.05)^4 + 3500/(1.05)^5 + 3500/(1.05)^6 + 3500/(1.05)^7 + 3500/(1.05)^8

= 3333.33 + 3174.60 + 3023.43 + 2879.45 + 2742.34 + 2611.75 + 2487.38 + 2368.93

Present value of benefits = $22,621.24

so,

Benefit - cost ratio = present value of benefits /present value of costs.

Benefit-cost ratio = 22,621.24/7500

= 3.01

Benefit ​​​​​- cost ratio = 3.01

Year	cash outflows	cash inflows
0	$7500
1	$0	$3500
2	$0	$3500
3	$0	$3500
4	$0	$3500
5	$0	$3500
6	$0	$3500
7	$0	$3500
8	$0	$3500