Hi!!
1. Janice Smith wishes to accumulate $8,000 by the end of 5 years by
making equal annual end-of-year deposits over the next five years. If
Janice can earn 7 percent on her investments, how much must she
deposit at the end of each year to meet this goal?
This is a Future value of an annuity case (ordinary), an invest of an
equal amount of money at the end of each year for a specified number
of years and allow it to grow at certain rate.
The formula for this calculation is:
FV = PMT * [( 1 + i )^N - 1] / i
Where:
FV = future value (maturity value)
PMT = payment per period
i = interest rate in percent per period
N = number of periods
In this problem:
FV = $8,000
PMT = unknown
i = 0.07
N = 5
Then:
PMT = FV * i / [( 1 + i )^N - 1] =
= $8,000 * 0.07 / [(1.07)^5 - 1] =
= $1,391.13
She must deposit $1391.13 at the end of each year to meet her goal.
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2. J& J just issued a bond with a $1,000 face value and a coupon rate
of 7%. If the bond has a life of 30 years, pays annual coupons and the
yield to maturity (YTM) is 6.8%, what will be the bond sell for?
Market value of a bond = PV of future payments (coupons and principal)
discounted at cost of debt (the yield to maturity); then:
Bond Price = Coupon/YTM * [(1 - (1 / (1+YTM)^30))] + Face/(1+YTM)^30 =
= $70/0.068 * [(1 - (1/(1.068)^30] + $1,000/(1.068)^30 =
= $886.37 + $138.95 =
= $1,025.32
The bond price is $1,025.32
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3. Biogenetics, Inc plans to retain and reinvest all of their
earnings for the next 30 years. Beginning in year 31, the firm will
begin to pay a $12.00 per share dividend. The dividend will not
subsequently change. Given a required return of 15%, what should the
stock sell for today?
30 years from now, the stock price will be:
P_30 = $12/0.15 = $80
Today price (P) is the PV of the P_30, i.e. you must discount this
lump sum (P_30) back to the present:
P = P_30 / (1.15)^30 =
= $80 / 66.21 =
= $1.21
Today stock's price is $1.21
See for reference "Stock Valuation Formula (DCF) and Calculator / Graph":
http://www.moneychimp.com/articles/finworks/fmvaluation.htm
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4. What is the NPV of a project that is expected to pay $10,000 a
year for 7 years if the initial investment is $40,000 and the required
return is 15%?
-PRESENT VALUE:
Present Value (PV) for cash flows made at the end of each period
(ordinary annuities):
CF1 CF2 CF7
PV = --------- + ---------- + ... + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^7
Where r is the required return and n is the number of periods.
If all the cash flows are equal (like in this problem):
CF 1
PV = ---- * [1 - ---------] =
r (1+r)^7
= $10,000/0.15 * [1 - 1/(1.15)^7] =
= $41,604.20
-NET PRESENT VALUE:
NPV = PV - I where I = Initial Investment
NPV = $41,604.20 - $40,000 =
= $1,604.20
The NPV of the project is $1,604.20
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5. A firm has 2,000,000 shares of common stock outstanding with a
market price of $2.00 per share. It has 2,000 bonds outstanding, each
selling for $1,200. The bonds mature in 15 years, have a coupon rate
of 10% and pay coupons annually. The firm?s beta is 1.2, the risk free
rate is 5%, and the market risk premium is 7%. The tax rate is 34%.
Calculate the WACC?
Market value of Equity = 2,000,000 * $2.00 = $4,000,000
Market value of Debt = 2,000 * $1,200 = $2,400,000
Total value = $4,000,000 + $2,400,000 = $6,400,000
Weight of equity (E/V) = 4M / 6.4M = 0.625
Weight of debt (D/V) = 2.4M / 6.4M = 0.375
Risk free rate = Rf = 5%
Market risk premium = Rp = 7%
Cost of Equity = RE = Rf + beta * Rp =
= 5% + 1.2 * 7% =
= 13.4% or 0.134
Cost of debt (RD):
N = 15,
Price = $1,200,
Face Value = not specified by the problem, I will assume $1,000,
Coupon = 10%*$1000 = $100,
Knowing that the bond price formula is:
Bond Price = Coupon/YTM * [(1 - (1 / (1+YTM)^15))] + Face/(1+YTM)^15
= PV of Coupons + PV of principal
To calculate the cost of debt (or YTM) consider the bond as a project
with an initial investment of $1,200 (today's price) and annual cash
flows of $100 at the end of the first 14 years and a final cash flow
of $1,100 (principal + coupon).
The IRR of this project is the YTM of the bond, just use an
spreadsheet or a calculator and you will get:
YTM = 7.7053%
Thus, RD = 7.7053% or 0.07053
To calculate WACC you must multiply the cost of each capital component
by its proportional weight and then sum:
WACC = (D/V)*Rd*(1-T) + (E/V)*Re =
= 0.375*0.077053*(1-0.34) + 0.625*0.134 =
= 10.28%
The WACC is 10.28%
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I hope that this helps you. Feel free to request for a clarification
if you need it.
Regards.
livioflores-ga |
