Hi!!
1. You invest $5,000 today at 8 percent interest compounded annually.
How much will you have at the end of 15 years?
FV = PV*(1 + i)^n
Where:
FV = Future Value
PV = Present Value
i = Interest Rate Per Period
n = Number of Compounding Periods
"Future Value":
http://www.getobjects.com/Components/Finance/TVM/fv.html
For this problem:
PV = $5,000
i = 8% = 0.08
n = 15 Periods
FV = $5,000*(1+0.08)^15 =
= $5,000*3.172 =
= $15,860
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2. Stephen Company has a project that requires $30,000 initial
investment and annual cash flow for 5 years of $10,000. The cost of
capital is 14%. What is the profitability index?
The profitability index of a project is the ratio between the present
value of the future cash flows and the initial investment required for
that project. It is also called the benefit-cost ratio:
PI = PV / I , PI gives the return per dollar invested.
Present Value formula:
CF1 CF2 CFn
PV = ----------- + ----------- + ... + ---------- ;
(1 + r)^1 (1 + r)^2 (1 + r)^n
where:
PV = Present Value
CFi = cash flow for year i
r = cost of capital
n = Number of years
When all cash flows are equal we have that:
PV = CF/r * [1 - 1/(1+r)^n] =
= 10,000/0.14 * [1 - 1/(1.14)^5] =
= 10,000/0.14 * [0.48063] =
= 34,330.81
PI = PV / I =
= 34,330.81 / 30,000 =
= 1.14
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3. A company issued $1,000 face value bonds with a 9 percent annual
coupon payments and 20 years remaining to maturity. If the yield to
maturity is 12%, what is the current value of the bond?
The value of a bond is the Present Value of all the future payments
(Coupons + Principal), the discount rate to calculate this PV in this
case is the yield to maturity = 12%:
Coupon Payments = C = $1,000 * 0.09 = $90
For these bonds the formula for the present value of the 20 coupon
payments is the formula used to calculate the PV of a regular 20 years
annuity:
PV coupons = Coupon/Y * [(1 - (1 / (1+Y)^20))] =
= $90/0.12 * [(1 - (1 / (1.12)^20))] = (use a calculator here)
= $672.25
For reference on the formula see:
http://www.netmba.com/finance/time-value/annuity/
PV of principal = Face Value / (1+Y)^20 =
= $1,000 / (1.12)^20 = (use a calculator here)
= $103.67
Bond value = PV coupons + PV of principal =
= $672.25 + $103.67 =
= $775.92
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4. Assume you can receive $25,000 5 years from today. How much should
you accept today assuming an 8 percent rate of return?
You know the future value of a payment and need to know its present value:
PV = FV/(1+r)^n =
= 25,000 / (1.08)^5 =
= 17,014.58
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5. Jazz Corporation sells picture frames for $10 each. The variable
cost of each frame is $6. Fixed costs are $20,000.
a) What is the break-even point in units?
Break-even = Fixed Costs / Contribution margin per unit
where:
Contribution margin per unit = (Revenues - Variable Costs) / Units sold =
= Price per unit - Variable cost per unit =
= $10 - $6 =
= $4
Then:
Break-even = $20,000 / $4 = 5,000 units
b) Compute the sales level in units required to earn a target
operating income of $50,000.
Net Income = Revenues - Expenses =
= Revenues - Variable costs - Fixed costs =
= Units sold * Sale price - Units sold * Variable cost per unit -
- Fixed costs =
= Units sold * Contribution margin per unit - Fixed costs =
Then:
Units sold = (Net Income + Fixed costs )/Contribution margin per unit =
= ($50,000 + $20,000)/$4 =
= 17,500 units.
Note that if you use the last formula for a Net Income equal to zero
you are calculating the break-even point in units.
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6. A 25 year old student wants to retire at 65. He plans to save
$2,000 each year earning 8 percent interest. If he makes these
deposits each year until he retires, how much would he have saved?
Here you want to know the future value of a 40 years annuity:
FV = PMT/i * [(1 + i)^n - 1] =
= 2,000/0.08 * [1.08^40 - 1] =
= 25,000 * 20.7245 =
= 518,113.04
He will save $518,113.04
See for references:
"Future Value of an Annuity":
http://www.getobjects.com/Components/Finance/TVM/fva.html
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7. A company is investing $100,000 in a piece of equipment with a
5-year useful life. Below are the estimated cash inflows. Assume an
11 percent cost of capital.
Year Cash Inflow
1 35000
2 25000
3 30000
4 15000
5 40000
a.) Calculate the payback period (assume all cash flows are received
evenly throughout the year and round answer to the nearest month)
PayBack Period:
Payback Period (PB) calculation give us an idea on how long it will
take for a project to recover the initial investment.
If Y is the year before the full recovery of the investment I, U is
the unrecovered cost at the start of last year, and CFi is the CF of
the year Y+1 then:
PB = Y + U/CFi
Note that at the end of the third year the initial investment is not
recovered, but at the end of the fourth it was, so the payback period
is greater than 3:
Y = 3
U = 100,000 - 35,000 - 25,000 - 30,000 = 10,000
CF4 = $15,000
Then:
PB = 3 + 10,000/15,000 = 3 + 2/3
Note: Each month is the 1/12 part of the year, then 2/3 of a year is
the month 12*2/3 = 8 .
The payback period is 3 years and 8 months.
b.) Calculate the net present value.
Present Value formula:
CF1 CF2 CFn
PV = ----------- + ----------- + ... + ---------- ;
(1 + r)^1 (1 + r)^2 (1 + r)^n
where:
PV = Present Value
CFi = cash flow for year i
r = cost of capital
n = Number of years
NPV = PV - I , where I is the initial investment.
Using a calculator you will find that PV = $107,376.85 , then:
NPV = $107,376.85 - $100,000 = $7,376.85
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8. Simon, Inc. has the following capital structure. Its corporate tax
rate is 40%. What is its WACC?
Security Market Value Required Rate of Return
Debt $30 million 8.0%
Preferred Stock $10 million 6.0%
Common Stock $40 million 10.0%
Total $80 million
To calculate WACC you must multiply the cost of each capital component
by its proportional weight and then sum, the resulted formula is:
WACC = Wd*Kd*(1-Tax) + Ws*Ks + Wp*Kp ;
where:
Wd = weight of debt = $30m/$80m = 0.375 or 37.5%
Ws = weight of common stocks = $40m/$80m = 0.50 or 50%
Wp = weight of preferred stocks = $10m/$80m = 0.125 or 12.5%
Kd = cost of debt = 8%
Ks = cost of common stocks = 10%
Kp = cost of preferred stocks = 6%
WACC = 0.375*0.08*(1-0.4) + 0.5*0.1 + 0.125*0.06 =
= 0.375*0.08*0.6 + 0.5*0.1 + 0.125*0.06 =
= 0.0755
The WACC is 7.55% .
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9. XYZ Company is purchasing research equipment costing $60,000. It
is financed with a 14% loan requiring end of the year payments of
$25,844 for 3 years. Calculate the annual interest expense for 3
years.
At the end of the first period interest has accrued, the interest rate
per period is 14%, and the balance at this point is $60,000, so the
accrued interest is:
I_1 = 0.14*$60,000 = $8,400
After the first payment the loan balance is: $25,843.89
B1 = 60,000 + I_1 - 25,844 =
= 60,000 + 8,400 - 25,844 =
= 42,556
At the end of the second period we add the interest on the previous
balance (B1) that is:
I_2 = 0.14 * $42,556 = $5957.84
The new balance is:
B2 = B1 + I_2 - Payment =
= 42,556 + 5,957.84 - 25,844 =
= 22,669.84
At the end of the last period (3rd) the accrued interest is:
I_3 = 0.14 * $22,669.84 = $3,173.78
After the 3rd payment the final balance must be zero, in effect:
B3 = B2 + I_3 - Payment =
= 22,669.84 + 3,173.78 - 25,844 =
= -0.38 (there are some rounding errors,starting at the amount of
payment, it must be $25,843.89 for a 14% loan of $60,000).
The interest expenses for each year are:
I_1 = $8,400.00
I_2 = $5,957.84
I_3 = $3,173.78
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10. A firm's stock has a beta of 2. The risk free rate is 5% and the
market risk premium is 7%. Calculate the expected rate of return on
the stock.
According to the CAPM:
E = rf + Beta * Market risk premium
where
E = the expected return on the security
rf = the risk-free rate
Then:
E = 5% + 2 * 7% = 19%
The expected return on the company's stocks is 19% .
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I hope that this helps you, I answer this question based in my own knowledge.
Before rate this answer feel free to request for a clarification if you need it.
Regards,
livioflores-ga |
