3. A firm has 5,000,000 shares of common stock outstanding, each with a market p
ID: 2751562 • Letter: 3
Question
3. A firm has 5,000,000 shares of common stock outstanding, each with a market price of $8.00 per share. It has 25,000 bonds outstanding, each selling for $1,100 with a $1,000 face value. The bonds mature in 12 years, have a coupon rate of 9 percent, and pay coupons semi-annually. The firm's equity has a beta of 1.4, and the expected market return is 15 percent. The tax rate is 35 percent and the WACC is 14 percent. Calculate the risk-free rate. 4. You are trying to pick the least-expensive machine for your company. You have two choices: machine A, which will cost $100,000 to purchase and which will have OCF of -$7,000 annually throughout the machine's expected life of three years; and machine B, which will cost $125,000 to purchase and which will have OCF of -$2,600 annually throughout that machine's four-year life. Both machines will be worthless at the end of their life. If you intend to replace whichever type of machine you choose with the same thing when its life runs out, again and again out into the foreseeable future, and if your business has a cost of capital of 15 percent, which one should you choose?
year 0 1 2 3 4 Machine A CF's -$100000 -$7000 -$7000 -$7000 Machine B CF's $125,00 -$2600 -$2600 -$2600 -$2600Explanation / Answer
3./
WACC= WEIGHT OF EQUITY * Ke + WEIGHT OF DEBT * Kd
Ke= COST OF EQUITY
Kd= COST OF DEBT
IN THIS QUESTION WE HAVE USED THE MARKET WEIGHT FOR CALCULATION
TOTAL EQUITY IN MARKET PRICE (5000000 * $8.00) =$40000000
TOATAL DEBT OR BOND IN MARKET PRICE (25000 * $1100) =$27500000
TOTAL =$67500000
WEIGHT OF EQUITY = $40000000 / $67500000 *100
59.26%
WEIGHT OF DEBT =$27500000 / $67500000 *100
=40.74%
AFTER TAX Kd= Kd(1 - TAX RATE)
= 0.09(1 - 0.35)
=5.85%
SO, WACC= (0.5926 * Ke) + (0.4074 * 5.85%)
0.14 =(0.5926 * Ke) + 0.0238329
Ke=0.14 - 0.0238329 /0.5926
=19.60%
Ke= Rf + BETA(Rm -Rf)
Rf= RISK FREE INTEREST
Rm= MARKET RETURN
SO, 19.60%=Rf + 1.4(15% - Rf)
19.60%=Rf +21% - 1.4Rf
0.4Rf=1.40%
Rf=1.40% / 0.4
Rf =3.5%
4./
MACHINE A
YEAR CASH FLOW DISCOUNTING FACTOR@15% DISCOUNTED CASH FLOW
0 ($100000) 1.000 ($100000)
1 ($7000) 0.8695 ($6086)
2 ($7000) 0.7561 ($5293)
3 ($7000) 0.6575 ($4602)
NPV OF COST =($115981)
MACHINE A
YEAR CASH FLOW DISCOUNTING FACTOR@15% DISCOUNTED CASH FLOW
0 ($125000) 1.000 ($125000)
1 ($2600) 0.8695 ($2261)
2 ($2600) 0.7561 ($1966)
3 ($2600) 0.6575 ($1709)
4 ($2600) 0.5717 ($1486)
NPV OF COST =($132422)
AS THE LIFE OF THE TWO PROJECT IS DIFFRENT WE HAVE TO CALCULATE EQUATED ANNUAL COST (EAC) FOR EACH PROJECT AND THE PROJECT WITH LOWEST EQATED ANNUAL COST (EAC) SHOULD BE SELECTED.
EAC= NPV OF COST / PVAF
PVAF= PRESENT VALUE ANNUITY FACTOR
EAC OF PROJECT A= NPV OF COST / PVAF @15% FOR 3YEARS
=115981/2.283
=$50802
EAC OF PROJECT B= NPV OF COST / PVAF @15% FOR 4YEARS
=132422/2.855
=$46382
AS PROJECT B HAS LOWEST EAC , SELECTED.
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