Question
In: Finance
You are considering opening a drive-in movie theater and running it for ten years. You have...
You are considering opening a drive-in movie theater and running it for ten years. You have spent after-tax $10,000 researching the land that will be used for theater, but if you take the project you expect to incur another immediate after-tax expense of $20,000 as you work with a consulting firm to decide how to most efficiently run the business.
The project entails an immediate $100,000 capital expenditure, which can be depreciated over 10 years. You expect to sell this capital investment for $25,000 at the end of the ten year project. Working capital expenses for the project are $50,000 immediately, $40,000 incurred two years from today, both of which are fully recovered in ten years (at the end of the project).
The project’s operating costs are expected to be $100,000 for each of the first five years and then (starting between t=5 and t=6) grow at -5% per year through the end of the project (i.e., through t=10). You expect the project’s revenues to start at $100,000 starting one year from today and remain constant for the life of the project.
- (1 points) To determine the discount rate for the project, you have found an all-equity firm with a risk level similar to the company you’re starting. That firm’s equity has a standard deviation of returns of 35% and a correlation with the stock market of 0.8. The risk free rate is 4%, the expected market returns are 9.5% and the standard deviation of market returns is 28%. What is your estimated cost of capital?
- (7 Points) You decide to use 10% as the project’s opportunity cost of capital (ignore your answer from part a). Your expected tax rate is 25%. What is the project’s NPV?
- (2 points) You find out that the government is interested in buying the capital investment from you at the end of the project. Instead of selling it for $25,000 at the end of the project, the government will commit today to buying the capital from you for $75,000 post-tax ten years from today. You trust the government and think that this sale is risk free should you take the project. To what extent (if any) should the above information factor in to your decision regarding whether or not to open the theater? Does it change the NPV in any way, if so how? (hint: think of the capital investment as its own project – how will this affect the cash flows and/or the discount rate)
Can you add as much details as you can, Thank you!
Solutions
Expert Solution
| Present Value(PV) of Cash Flow: | |||||||||||||
| (Cash Flow)/((1+i)^N) | |||||||||||||
| i=discount rate =10%=0.1 | |||||||||||||
| N=Year of Cash Flow | |||||||||||||
| Amount of $10000 already spent is sunk cost and not relevant | |||||||||||||
| CASH FLOW ANALYSIS OF THE PROJECT | |||||||||||||
| N | Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| a | Cash Flow for fixed asset investment | -$100,000 | |||||||||||
| b | Immediate after tax cash expense | -$20,000 | |||||||||||
| c | Initial cash flow for working capital | -$50,000 | |||||||||||
| D=a+b+c | Total initial cash flow | -$170,000 | |||||||||||
| e | Annual Revenues | $100,000 | $100,000 | $100,000 | $100,000 | $100,000 | $100,000 | $100,000 | $100,000 | $100,000 | $100,000 | ||
| f | Annual Operating Costs | -$100,000 | -$100,000 | -$100,000 | -$100,000 | -$100,000 | -$95,000 | -$90,250 | -$85,738 | -$81,451 | -$77,378 | ||
| g | Annual Depreciation expense (100000-25000)/10 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | ||
| h=e+f+g | Before tax operating profit | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$7,500 | -$2,500 | $2,250 | $6,763 | $11,049 | $15,122 | ||
| i=-h*25% | Tax (Expenses)/Savings | $1,875 | $1,875 | $1,875 | $1,875 | $1,875 | $625 | -$563 | -$1,691 | -$2,762 | -$3,780 | ||
| j=h+i | After tax operating profit | -$5,625 | -$5,625 | -$5,625 | -$5,625 | -$5,625 | -$1,875 | $1,688 | $5,072 | $8,287 | $11,341 | ||
| k | Add depreciation expenses(non cash) | $7,500 | $7,500 | $7,500 | $7,500 | $7,500 | $7,500 | $7,500 | $7,500 | $7,500 | $7,500 | ||
| L=j+k | Annual Operating Cash Flow | $1,875 | $1,875 | $1,875 | $1,875 | $1,875 | $5,625 | $9,188 | $12,572 | $15,787 | $18,841 | ||
| M | After tax salvage value | $25,000 | |||||||||||
| P | Working capital Cash Flow | -$40,000 | $90,000 | ||||||||||
| CF=D+L+M+P | Net Cash Flow | ($170,000) | $1,875 | ($38,125) | $1,875 | $1,875 | $1,875 | $5,625 | $9,188 | $12,572 | $15,787 | $133,841 | SUM |
| PV=CF/(1.1^N) | Present Value of Net Cash Flow | ($170,000) | $1,705 | ($31,508) | $1,409 | $1,281 | $1,164 | $3,175 | $4,715 | $5,865 | $6,695 | $51,602 | ($123,899) |
| NPV=Sum of PV | Net Present Value(NPV) | ($123,899) | |||||||||||
| If Salvage Value is $75000 instead of $25000 | |||||||||||||
| Difference in Salvage Value=(75000-25000) | $50,000 | ||||||||||||
| Present Value of the difference=50000/(1.1^10)= | $19,277 | ||||||||||||
| NPV is increased by $19277 | |||||||||||||
| Still the NPV will be negative |
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