Question
In: Finance
Given the following two projects and their cash flows, , calculate the discounted payback period with...
Given the following two projects and their cash flows,
, calculate the discounted payback period with a discount rate of 6%, 8%,and 18%.
What do you notice about the payback period as the discount rate rises? Explain this relationship.
With a discount rate of 6%,
the cash outflow for project A is:
A. recovered in 5 years.
B.recovered in 3.16 years.
C.recovered in 3 years.
D.never fully recovered.
|
Cash Flow |
A |
B |
||
|
Cost |
$8,000 |
$100,000 |
||
|
Cash flow year 1 |
$2,857 |
$10,000 |
||
|
Cash flow year 2 |
$2,857 |
$20,000 |
||
|
Cash flow year 3 |
$2,857 |
$30,000 |
||
|
Cash flow year 4 |
$2,857 |
$40,000 |
||
|
Cash flow year 5 |
$2,857 |
$15,000 |
||
|
Cash flow year 6 |
$2,857 |
$0 |
||
Solutions
Expert Solution
Using excel formula to calculate discounted pay back period
| Year | 0.00 | 1 | 2 | 3 | 4 | 5 | 6 |
| Project A Disount Rate =6% | -8000 | 2857 | 2857 | 2857 | 2857 | 2857 | 2857 |
| Discounted Cash Flow | -8000.00 | 2695.28 | 2542.72 | 2398.79 | 2263.01 | 2134.92 | 2014.07 |
| Cumulative Cash flow | -8000.00 | -5304.72 | -2762.00 | -363.20 | 1899.81 | 4034.72 | 6048.80 |
| Discounted Payback Period | 3.16 | ||||||
| excel formula | (=3-363.20/2263.01) | ||||||
| Year | 0.00 | 1 | 2 | 3 | 4 | 5 | 6 |
| Project A Disount Rate =8% | -8000 | 2857 | 2857 | 2857 | 2857 | 2857 | 2857 |
| Discounted Cash Flow | -8000.00 | 2645.37 | 2449.42 | 2267.98 | 2099.98 | 1944.43 | 1800.39 |
| Cumulative Cash flow | -8000.00 | -5354.63 | -2905.21 | -637.23 | 1462.75 | 3407.17 | 5207.57 |
| Discounted Payback Period | 3.30 | ||||||
| excel formula | (=3+637.23/2099.98) | ||||||
| Year | 0.00 | 1 | 2 | 3 | 4 | 5 | 6 |
| Project A Disount Rate =18% | -8000 | 2857 | 2857 | 2857 | 2857 | 2857 | 2857 |
| Discounted Cash Flow | -8000.00 | 2421.19 | 2051.85 | 1738.86 | 1473.61 | 1248.82 | 1058.32 |
| Cumulative Cash flow | -8000.00 | -5578.81 | -3526.96 | -1788.10 | -314.49 | 934.33 | 1992.65 |
| Discounted Payback Period | 4.25 | ||||||
| excel formula | (4+314.49/1248.82) |
| Year | 0.00 | 1 | 2 | 3 | 4 | 5 | 6 |
| Project B Discount Rate =6% | -100000 | 10000 | 20000 | 30000 | 40000 | 15000 | 0 |
| Discounted Cash Flow | -100000.00 | 9433.96 | 17799.93 | 25188.58 | 31683.75 | 11208.87 | 0.00 |
| Cumulative Cash flow | -100000.00 | -90566.04 | -72766.11 | -47577.53 | -15893.78 | -4684.91 | -4684.91 |
| Discounted Payback Period | Never Recovered | ||||||
| excel formula | |||||||
| Year | 0.00 | 1 | 2 | 3 | 4 | 5 | 6 |
| Project B Discount Rate =8% | -100000 | 10000 | 20000 | 30000 | 40000 | 15000 | 0 |
| Discounted Cash Flow | -100000.00 | 9259.26 | 17146.78 | 23814.97 | 29401.19 | 10208.75 | 0.00 |
| Cumulative Cash flow | -100000.00 | -90740.74 | -73593.96 | -49779.00 | -20377.80 | -10169.06 | -10169.06 |
| Discounted Payback Period | Never Recovered | ||||||
| excel formula | |||||||
| Year | 0.00 | 1 | 2 | 3 | 4 | 5 | 6 |
| Project B Discount Rate =18% | -100000 | 10000 | 20000 | 30000 | 40000 | 15000 | 0 |
| Discounted Cash Flow | -100000.00 | 8474.58 | 14363.69 | 18258.93 | 20631.56 | 6556.64 | 0.00 |
| Cumulative Cash flow | -100000.00 | -91525.42 | -77161.74 | -58902.81 | -38271.25 | -31714.62 | -31714.62 |
| Discounted Payback Period | Never Recovered | ||||||
| excel formula |
At 6% Project A would be recovered in 3.16 years (Option b is correct option)
jeff jeffy answered 2 years agoRelated Solutions
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