# Present Value Calculations Discount Rate

Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years:

Year 1: $42,000,000

Year 2: $62,000,000

Year 3: $99,000,000

Compute the present value of this stream of income at a discount rate of 8%. Remember, you are calculating the present value for a whole stream of income, i.e. the total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this oil well at a 8% discount rate but you have to show how you got to this number.

Now compute the present value of the income stream from the gold mine at a discount rate of 6%, and at a discount rate of 4%. Compare the present values of the income stream under the three discount rates.

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Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years:

Year 1: $42,000,000

Year 2: $62,000,000

Year 3: $99,000,000

Compute the present value of this stream of income at a discount rate of 8%. Remember, you are calculating the present value for a whole stream of income, i.e. the total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this ...

#### Solution Summary

Computes the present value of a stream of income and compares the present values of the income stream under three discount rates.

leasing vs buying, break-even analysis

5.4

You want to buy a new car, but you're not sure whether you should lease it or buy it. You can buy it for $50,000, and you expect that it will be worth $20,000 after you use it for 3 years. Alternatively, you could lease it for payments of $650 per month for the 3-year term, with the first payment due immediately. The lease company did not tell you what interest rate they're using to calculate the monthly payments, but you know you could borrow money from your banker at an annual percentage rate (APR) of 8%.

A. Calculate the present value of the lease payments, assuming monthly compounding at the given APR of 8%.

B. Calculate the present value of the $20,000 salvage value, again using monthly compounding and the given APR of 8%. Which option do you prefer, lease or buy?

C. Calculate the amount of the salvage value which would make you indifferent between leasing and buying.

D. If you were able to use this car 100% for business, rendering the lease payments tax-deductible, or alternatively, allowing you to deduct depreciation using straight-line depreciation (depreciated to expected salvage value) and assuming your tax rate is 40%, would you prefer to buy or lease the car?

6.1 You and your friends are thinking about starting a motorcycle company named Apple Valley Choppers. Your initial investment would be $500,000 for depreciable equipment, which should last 5 years, and your tax rate would be 40%. You could sell a chopper for $10,000, assuming your average variable cost per chopper is $3000, and assuming fixed costs, such as rent, utilities and salaries, would be $200,000 per year.

A. Accounting breakeven: How many choppers would you have to sell to break even, ignoring the costs of financing?

B. Financial breakeven: How many choppers would you have to sell to break even, if you required a 15% return? (Hint: Use the 15% as the discount rate and calculate net present value. In Excel, you may want to use the Goal Seek command, or simply use trial and error to find the correct amount.)

C. Assuming you could sell 60 choppers per year, what would be your IRR?

D. Assuming you could sell 60 choppers per year, what would your selling price have to be to generate a net present value of $150,000 at a 15% discount rate?

E. If you could sell 60 choppers in the first year, and your sales volume increased by 5% each year until the end of year 5, what would the net present value be at a 15% discount rate?

F. If you need to invest working capital equal to 10% of the next (coming) year's sales revenue, what would be the effect on the net present value of the project? Do you think that working capital investments always reduce the net present value of projects? (Assume a 15% discount rate, and sales volume increases by 5% each year.)

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