Question

What do you notice about the payback period as the discount rate rises? Explain this relationship

Cash flow A B
Cost $8,000 $90,000
Cash flow year 1 $2,857 $9,000
Cash flow year 2 $2,857 $18,000
Cash flow year 3 $2,857 $27,000
Cash flow year 4 $2,857 $36,000
Cash flow year 5 $2,857 $13,500
Cash flow year 6 $2,857 $0
1. With a discount rate of 4%, the cash outflow for project A is:________.
2. Discount rate of 12%, the cash outflow for project B is:________.
3. Discount rate of 20%, the cash outflow for project B is:________.
4. As the discount rate increased, the discount payback perioud_______. The reason is that the future dollars are worth______in present value as the discount rate increases requiring______future dollars to recover the present value of the outlay.

Answer 1

Payback Period as the discount rate rises

1. With a discount rate of 4%, the cash outflow for project A is:__$8,000______.

2. Discount rate of 12%, the cash outflow for project B is:__$90,000______.

3. Discount rate of 20%, the cash outflow for project B is:__$90,000______.

4. As the discount rate increased, the discounted payback perioud__increased_____. The reason is that the future dollars are worth__less____in present value as the discount rate increases requiring__more____future dollars to recover the present value of the outlay.

Step-by-step explanation:

a) Data and Calculations:

Cash flow A B Discount Discount

Factor at 12% PV Factor 20% PV

Cost $8,000 $90,000

Cash flow year 1 $2,857 $9,000 0.893 $8,037 0.833 $7,497

Cash flow year 2 $2,857 $18,000 0.797 14,346 0.694 12,492

Cash flow year 3 $2,857 $27,000 0.712 19,224 0.579 15,552

Cash flow year 4 $2,857 $36,000 0.636 22,896 0.482 17,352

Cash flow year 5 $2,857 $13,500 0.567 7,655 0.402 5,427

Cash flow year 6 $2,857 $0

PV at 4% 12% $72,158 20% $58,320

Annuity for Project A

= $14,976 ($2,857 x 5.242) at year 6

= $12,719 ($2,857 x 4.452) at year 5

= $10,371 ($2,857 x 3.630|) at year 4

= $7,928 ($2857 x 2.775) at year 3