Discounted Cash Flow Valuations and Net Present Value
Prob. 1
| Annuity | |||||
| 1 | 2 | 3 | |||
| Discount rate | Given | Given | Given | Best choice? | |
| Growth rate | Given | Given | Given | ||
| NPV | |||||
| IRR | |||||
| Cash flows: | |||||
| Start | Given | Given | Given | ||
| Year 1 | Given | ||||
| Year 2 | |||||
| Year 3 | |||||
| Year 4 | |||||
| Year 5 | |||||
| Year 6 and on |
Melinda Swigart:
Calculate using the NPV formula
Melinda Swigart:
Calculate Using the NPV formula
Melinda Swigart:
Remember to calculate the growth rate and add it to the previous periods cash flow. To calculate growth rate multiply the previous year's cash flow by 1+ the growth rate.
Melinda Swigart:
This will be the same formula until you get to Year 6 and on. Then you will need to use the formula for a perpetuity.
Melinda Swigart:
The formula for a growing perpetuity is on page 106 of your text book. It is PV = C/r-g. Refer to example 4.19.
Melinda Swigart:
There is no growth rate for the first one, so it is just a steady cash flow.
Prob. 2
| Software | Extended Plan | |||
| Discount rate | Given | Given | ||
| Growth rate | Given | Given | Text answer here. | |
| NPV | ||||
| IRR | ||||
| Cash flows: | ||||
| Start | Given | Given | ||
| Year 1 | Given | Given | ||
| Year 2 | ||||
| Year 3 | ||||
| Year 4 | ||||
| Year 5 | ||||
| Year 6 | ||||
| Year 7 | ||||
| Year 8 |
Melinda Swigart:
Use the NPV Formula
Melinda Swigart:
Use the IRR Formula
Prob. 3
| Rental Property | |||
| Discount rate | Given | ||
| Growth rate | Given | ||
| NPV | Text answer here. | ||
| IRR | |||
| Cash flows: | |||
| Start | Given | ||
| Year 1 | Given | ||
| Year 2 | |||
| Year 3 and on |
Melinda Swigart:
NPV Formula
Melinda Swigart:
IRR Formula
Melinda Swigart:
Don't forget to add the growth rate to the year 1 payment
Melinda Swigart:
Remember, in the perpetuity formula, you will first calcualte the cash inflow for the last year given (year 2 in this case), then you will raise this to the second power (^2), then you
divide by the rate minus the growth.
Prob. 4
| July 2000 pay due | Given | ||
| Interest rate | Given | ||
| Future value of July 2000 pay on July 1, 2011 | |||
| Present value of 25 yearly payments | Text answer here. | ||
| Year 1 | Given | ||
| Year 2 | |||
| Year 3 | |||
| Year 4 | |||
| Year 5 | |||
| Year 6 | |||
| Year 7 | |||
| Year 8 | |||
| Year 9 | |||
| Year 10 | |||
| Year 11 | |||
| Year 12 | |||
| Year 13 | |||
| Year 14 | |||
| Year 15 | |||
| Year 16 | |||
| Year 17 | |||
| Year 18 | |||
| Year 19 | |||
| Year 20 | |||
| Year 21 | |||
| Year 22 | |||
| Year 23 | |||
| Year 24 | |||
| Year 25 |
Melinda Swigart:
Read the problem carefully. What does it say he is paid each year? Enter this amount for the remaining years.
Melinda Swigart:
This is the NPV of all the future cash flows. Treat Year 1 as the cash outflow in the formla.
Melinda Swigart:
Refer to Example 4.3 in your text book.
Prob. 5
| Sale price (M$) per plane | Given | |||||||||||
| Down payment (%) | Given | |||||||||||
| Cost per plane (M$) | Given | |||||||||||
| Discount rate | Given | |||||||||||
| Years | ||||||||||||
| (in Million $) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| # of planes sold | ||||||||||||
| Investment | Given | Given | Given | |||||||||
| Revenues | ||||||||||||
| Production Costs | ||||||||||||
| Cash Flow | Given | Given | Given | |||||||||
| NPV | ||||||||||||
| IRR |
Melinda Swigart:
Use the NPV formula here, but because you have three cash outflows in the beginning you will not add the negative cash flow at the end. Instead these will be included in the range.
Melinda Swigart:
Use the IRR formula
Melinda Swigart:
The first two years revenue will just be the down payment.
Melinda Swigart:
If you read the problem closely it indicates that the down payments are collected and then 2 years later the remaining 24.5m So in year 6 they will collect the down payment for 50 planes, plus the remaining portion due on the 25 planes sold in year 4.
Melinda Swigart:
Production costs are the cost per plane given above. In year 4 they sold 25 planes.
v. MAR 2021
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