# Discounted cash flow problem

A 100-acre tract of land within an urban municipality is scheduled to be subdivided into 320 home sites, averaging 80 feet road frontage. There is active demand for homes in the $120,000 to $140,000 price bracket. The average price of dwellings planned for the subject tract is $125,000. The ratio of site to property value in similar subdivisions is 1 to 5 ($1 land to $4 building investment).

The proposed subdivision is to be improved with all required county utilities, including 60-foot wide paved roads fitted with concrete curbs and gutters, storm water drainage, water, and sewerage systems. Telephone and electric service, including streetlights, are to be supplied through underground cables laid in heavy-gauge PVC conduits.

Analysis of development plans indicates total development costs per lot are:

Development costs $8,500

Underground electric utility lines 1,200

Engineering 800

Development fee 4,076

Interest, taxes, legal fees 500

$15,076

Sales commission (10%)

Average first year lot price $26,000

Annual rate of increase in lot prices 6%

Expected yield to developer 12%

Lot sales are forecast to be 60 lots per year for years 1-5 and 20 lots in year 6.

The following information should also be considered:

Water and sewer distribution connections are estimated at $400 per lot. The developer is to receive a refund of $200 under county regulations at the time each lot is connected into the municipal system and becomes activated by customer use.

No extra cost for telephone lines or site connection is chargeable to the developer.

Advertising and field overhead costs are estimated at 3.0 percent of gross sales.

Based on market analysis and the information presented herein, derive the value of the undeveloped tract under alternative options as follows:

1. The development for the entire 320-lot subdivision is to be completed and all utilities installed during the first year. What price could an investor afford to pay for this land on the development program described previously?

2. Suppose that the developer chose to spread out his costs equally per year over 3 years. What effect would this have on the present value of the property?

3. Explain which development program you would advise the developer to select.

The development costs, electric utility lines, development fee, engineering and water/sewer distribution costs are allocated as set forth in the above two options. However, interest, taxes, legal fees, sales commission, advertising and field overhead costs, and water and sewer connection fee rebates are computed as sales occur.

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#### Solution Preview

Hello!

I've attached an Excel file with your solution. Let me explain each item.

The number of lots sold each year should be self-explanatory.

Lot price starts at $26,000 and increases 6% per year

Revenue is simply (Lots Sold)*(Lot price)

Regarding costs, I separated them in "type I" and "type II". Type I costs are the costs that, according to the problem, "are allocated as set forth in the two options". Type II costs are the ones that are computed as sales occur.

Notice that after the "Costs - Type I" table, I included a "Total Lots" row. This row is just to tell Excel if it should put all these costs in the 1st year (so it's 320 lots times the cost per lot, in ...

#### Solution Summary

The expert explains which development program you would advise the developer to select.

Integrative Problem Chapter 22 Questions and Chapter 21 problem #3

Integrative Problem Chapter 22 Questions

1. You purchase machinery for $23,958 that generates cash flow of $6,000 for five years. What is the internal rate of return on the investment?

2. The cost of capital for a firm is 10 percent. The firm has two possible investments with the following cash inflows:

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A B

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Year 1 $300 $200

2 200 200

3 100 200

a. Each investment costs $480. What investment(s) should the firm make according to net present value?

b. What is the internal rate of return for the two investments?

Which investment(s) should the firm make?

Is this the same answer you obtained in part a?

c. If the cost of capital rises to 14 percent, which investment(s) should the firm make?

3) A firm has the following investment alternatives:

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Cash Inflows

A B C

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Year 1 $1,100 $3,600 -

2 1,100 - -

3 1,100 - $4,562

Each investment costs $3,000; investments B and C are mutually exclusive, and the firm's cost of capital is 8 percent.

a. What is the net present value of each investment?

b. According to the net present values, which investment(s) should the firm make?

Why?

c. What is the internal rate of return on each investment?

d. According to the internal rates of return, which investment(s) should the firm make?

Why?

e. According to both the net present values and internal rates of return, which investments should the firm make?

f. If the firm could reinvest the $3,600 earned in year one from investment B at 10 percent, what effect would that information have on your answer to part e?

Would the answer be different if the rate were 14 percent?

g. If the firm's cost of capital had been 10 percent, what would be investment A's internal rate of return?

h. The payback method of capital budgeting selects which investment?

Why?

4. The chief financial officer has asked you to calculate the net present values and internal rates of return of two $50,000 mutually exclusive investments with the following cash flows:

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Project A Project B

Cash Flow Cash Flow

Year 1 $10,000 $ 0

2 25,000 22,000

3 30,000 48,000

If the firm's cost of capital is 9 percent, which investment(s) would you recommend?

Would your answer be different if the cost of capital were 14 percent?

Chapter 21

3. A firm's current balance sheet is as follows:

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Assets $100 Debt $10

Equity $90

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a. What is the firm's weighted-average cost of capital at various combinations of debt and equity, given the following information?

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Debt/Assets After-Tax Cost of Debt Cost of Equity Cost of Capital

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0% 8% 12% ?

10 8 12 ?

20 8 12 ?

30 8 13 ?

40 9 14 ?

50 10 15 ?

60 12 16 ?

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b. Construct a pro forma balance sheet that indicates the firm's optimal capital structure. Compare this balance sheet with the firm's current balance sheet.

What course of action should the firm take?

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Assets $100 Debt $?

Equity $?

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c. As a firm initially substitutes debt for equity financing, what happens to the cost of capital, and why?

d. If a firm uses too much debt financing, why does the cost of capital rise?

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