Question

1. We are evaluating a project that costs $1,950,000, has a six-year life and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 97,000 units per year. Price per unit is $41.25, variable cost per unit is $18.50 and fixed costs are $950,000 per year. An initial investment of $250,000 in net working capital will be required and it is assumed that this amount will be recovered at the end of the project. The tax rate is 21 percent and you have the following information about the capital structure of the firm. Do this problem in Excel and attach the spreadsheet.

Book Value of Debt	$2,500,000,000
Market Value of Debt	$3,750,000,000
Book Value of Equity	$3,500,000,000
Market Value of Equity	$4,500,000,000
Dividend that the company has just paid	$2.35
Growth rate of dividends	4%
Current stock price	$32.50
Bond information	Coupon rate = 4%, maturity = 10 years, maturity value =$1,000 and the current price is 1,080.25. Assume interest is paid semiannually

1. Calculate cash flow and NPV. What is the sensitivity of NPV to changes in the sales figure. Explain what your answer tells you about a 500-unit decrease in projected sales.
2. What is the sensitivity of OCF to changes in the variable cost figure? Explain what your answer tells you about a $1 decrease in estimated variable costs.

Answer 1

Answer 1:

Calculation of WACC:

Capital structure:

Market value of equity = $4.50 billion

Market value of debt = $3.75 billion

Total value = 4.50 + 3.75 = $8.25 billion

Cost of equity:

Cost of equity = (Dividend next year / Share price) + Growth rate = (2.35 * (1 + 4%) / 32.50) + 4% = 11.52%

Cost of debt:

PV = $1,080.25.

Maturity = 10 * 2 = 20 semiannual periods

Semiannual coupon = 1000 * 4%/2 = $20

Semiannual yield = RATE (nper, pmt, pv, fv, type)

= RATE (20, 20, - 1080.25, 1000, 0)

= 1.5311%

Cost of debt = 1.5311% * 2 = 3.0623%

WACC = Cost of equity * weight of equity + Cost of debt * (1 - tax rate) * weight of debt

= 11.52% * 4.50 / 8.25 + 3.0623% * (1 - 21%) * 3.75/ 8.25

=7.38%

WACC = 7.38%

Cash flows and NPV are calculated and given below (highlighted):

Answer 2:

Sensitivity to changes in sales figure:

Change if NPV due to 500 units decrease in sales units

= (- 500 *(41.25 - 18.50) * (1 - 21%) * (1 - 1/ (1 + 7.38%)^ 6) /7.38%

= - $42,235.42

Hence:

Decrease of 500 units in projected sales units will decrease NPV by $42,235.42

Answer 3:

Sensitivity of OCF to changes in variable cost figure:

If variable cost decreases by $1, new variable cost, contribution will increase by $1 per unit.

Change in OCF on $1 decrease in variable cost = $1 * 97000 * (1 - 21%) = $76,630

Decrease of $1 in variable cost will increase OCF by $76,630