B-158 SOLUTIONS
3. Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 of recapturing the
initial investment, so the payback for Project A is:
Payback = 1 + ($21,000 / $25,000) = 1.84 years
Project B has cash flows of:
Cash flows = $14,000 + 17,000 + 24,000 = $55,000
4. When we use discounted payback, we need to find the value of all cash flows today. The value today of
the project cash flows for the first four years is:
Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21
Value today of Year 2 cash flow = $5,300/1.142 = $4,078.18
Value today of Year 3 cash flow = $6,100/1.143 = $4,117.33
Value today of Year 4 cash flow = $7,400/1.144 = $4,381.39
To find the discounted payback, we use these values to find the payback period. The discounted first
year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is:
Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years
For an initial cost of $10,000, the discounted payback is:
Discounted payback = 2 + ($10,000 – 3,684.21 – 4,078.18)/$4,117.33 = 2.54 years
5. R = 0%: 3 + ($2,100 / $4,300) = 3.49 years
discounted payback = regular payback = 3.49 years
R = 5%: $4,300/1.05 + $4,300/1.052 + $4,300/1.053 = $11,709.97
$4,300/1.054 = $3,537.62