Question
In: Finance
Costco, Inc. is conducting a new project with the following estimated cash flows. The initial outlay...
Costco, Inc. is conducting a new project with the following estimated cash flows. The initial outlay is estimated to be $1,950,000, and the incremental cash flows generated by this project would be $650,000 per year for 7 years. The estimated required rate of return of the project is 6%.
a. Calculate the NPV.
b. Calculate the PI.
c. Calculate the IRR.
d. Should this project be accepted?
Solutions
Expert Solution
Part A:
NPV :
NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/
Rejected.
NPV < 0 , Project will be rejected.
| Year | CF | PVF @0.06 | Disc CF |
| 0 | $ -19,50,000.00 | 1.0000 | $ -19,50,000.00 |
| 1 | $ 6,50,000.00 | 0.9434 | $ 6,13,207.55 |
| 2 | $ 6,50,000.00 | 0.8900 | $ 5,78,497.69 |
| 3 | $ 6,50,000.00 | 0.8396 | $ 5,45,752.53 |
| 4 | $ 6,50,000.00 | 0.7921 | $ 5,14,860.88 |
| 5 | $ 6,50,000.00 | 0.7473 | $ 4,85,717.81 |
| 6 | $ 6,50,000.00 | 0.7050 | $ 4,58,224.35 |
| 7 | $ 6,50,000.00 | 0.6651 | $ 4,32,287.12 |
| NPV | $ 16,78,547.94 |
Part B:
| Profitability Index: |
| PI = PV of Cash inflows / PV of Cash Outflows |
| If PI > 1, Project will be accepted, |
| PI = 1, Indifference point. Project will be accepted/ Rejected. |
| PI < 1, Project will be rejected. |
| Year | CF | PVF @0.06 | Disc CF |
| 1 | $ 6,50,000.00 | 0.9434 | $ 6,13,207.55 |
| 2 | $ 6,50,000.00 | 0.8900 | $ 5,78,497.69 |
| 3 | $ 6,50,000.00 | 0.8396 | $ 5,45,752.53 |
| 4 | $ 6,50,000.00 | 0.7921 | $ 5,14,860.88 |
| 5 | $ 6,50,000.00 | 0.7473 | $ 4,85,717.81 |
| 6 | $ 6,50,000.00 | 0.7050 | $ 4,58,224.35 |
| 7 | $ 6,50,000.00 | 0.6651 | $ 4,32,287.12 |
| PV of cash Inflows | $ 36,28,547.94 | ||
| PV of cash Outflows | $ 19,50,000.00 | ||
| Profitability Index: | 1.86 |
Part C:
IRR :
IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash
Outflows.
IRR = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in disc rate ] * 1%
If IRR > Cost of Capital - Project can be accepted
IRR = Cost of Capital - Indifferebce Point - Project will be
accepted / Rejected
IRR < Cost of Capital - Project will be erejected
| Year | Cash Flow | PVF/[email protected] | PV of Cash Flows | PVF/[email protected] | PV of Cash Flows |
| 1-7 | $ 6,50,000.00 | 3.0087 | $ 19,55,631.00 | 2.9370 | $ 19,09,060.02 |
| PV of Cash Inflows | $ 19,55,631.00 | $ 19,09,060.02 | |||
| PV of Cash Oiutflows | $ 19,50,000.00 | $ 19,50,000.00 | |||
| NPV | $ 5,631.00 | $ -40,939.98 |
PVAF = Sum [ PVF(r%, n) ]
PVF (r%, n) = 1 / ( 1 + r)6n
r = Disc rate
n = Time gap
| IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1% |
| = 0.27 + [5631 / 46570.98 ] * 1% |
| = 0.27 + [0.12 ] * 1% |
| = 0.27 + [0.0012] |
| = 0.2712 |
Part D:
Project can be accepted as NPV >0, PI >1 & IRR > Cost ofcapital.
Pls do rate, if the answer is correct and comment, if any further assistance is required.
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