Question

Q1. Dinah, the operator of Dinah's Diner, wishes to choose between two alternative investments providing the following annual net cash inflows over the five-year investment period: Year Alternative 1 Alternative 2 $8,000 8,600 8,800 8,200 4,100 $ 4,200 5,800 8,500 11,500 12,100 a. Calculate the paypack time for each alternative, assuming initial investment of $33,000 under each alternative. (3 points) b. Using NPV at 12 percent, would either of them be a good investment for Dinah? (3 points)

Answer 1

a) Payback period is the time period required to recover the initial investment back. After the payback period profit will be generated.

Time	Alternative 1 (cash inflows) in $	Alternative 1 (cumulative value)	Alternative 2 (cash inflows) in $	Alternative 2 (cumulative value)
1	8000	8000	4200	4200
2	8600	16600	5800	10000
3	8800	25400	8500	18500
4	8200	33600	11500	30000
5	4100	37700	12100	42100

(Assumption - all the cash flows are evenly distributed)

Alternative 1

Initial investment is $33000

Payback period =

$3 + \frac{7600}{8200}$

= 3 + 0.927

= 3.93 years

Alternative 2

Initial investment is $33000

Payback period =

$4 + \frac{3000}{12100}$

= 4 + 0.248

= 4.25 years

	Alternative 1	Alternative 2
Payback period	= 3.93 years	4.25 years

b) NPV = present value of cash inflows - present value of cash outflow.

Discount rate = 12 %

Present value of cash outflow = $ 33000

Time	PVF (12%,n)	Alternative 1 (cash inflows) in $	Present value of alternative 1	Alternative 2 (cash inflows) in $	Present value of alternative 2
1	0.893	8000	7144	4200	3750.6
2	0.797	8600	6854.2	5800	4622.6
3	0.712	8800	6265.6	8500	6052
4	0.636	8200	5215.2	11500	7314
5	0.567	4100	2324.7	12100	6860.7
Total of cash inflow			27803.7 $		28599.9 $

NPV of alternative 1 = 27803.7 - 33000 = - 5196.3 $

NPV of alternative 2 = 28599.9 - 33000 = - 4400.1 $

At 12 % both the alternatives has negative NPV, therefore both the options should be rejected. Neither of them is good investment option.