Hi lostinpeoria!!
1. Using the information below, calculate the payback period and the NPV.
Cost of Capital = 13%
Initial Investment 100,000
Cash inflow 1 15,000
Cash inflow 2 20,000
Cash inflow 3 30,000
Cash inflow 4 35,000
Cash inflow 5 40,000
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
The initial investment is $100,000 and you will recover it during the
fourth year, then:
Y = 3
and
U = $100,000 - ($15,000 + $20,000 + $30,000) = $35,000
PB = 3 + $35,000/$35,000 = 4 years
The payback period is 4 complete years.
- NPV:
Present Value (PV):
CF1 CF2 CF5
PV = --------- + ---------- + ... + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^5
Where r is the required return (13% or 0.13 in this case)
Net Present Value (NPV):
NPV = PV - I where I = Total Initial Investment
First calculate the PV of the cash flows:
PV = $15,000/1.13 + $20,000/(1.13)^2 + $30,000/(1.13)^3 + $35,000/(1.13)^4 +
+ $40,000/(1.13)^5 =
= $13,274.34 + $15,662.93 + $20,791.50 + $21,466.16 + $21,710.40 =
= $92,905.33
NPV = PV - I = $92,905.33 - $100,000 = -$7,094.67 (NEGATIVE!!)
The net present value of this project is -$7,094.67 . Since it is
negative, you will lose money with this project.
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2. Using the information in question #7, the IRR is closest to:
a. 3.5%
b. 5.5%
c. 10.5%
d. 20.5%
NOTE: I am assuming that the "information in question #7" is the
information in previous question. Whatever be the info the resolution
method is the same. If you want you can post the correct info and I
will show you the answer as a clarification.
IRR is the discount rate r at which the NPV equals zero:
NPV = PV - I = 0
Then IRR is the discount rate r at which:
PV = I
So you must find the r that solves the following equation:
CF1 CF2 CF5
I = --------- + ---------- + ... + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^5
You can use different ways to calculate the IRR, for example:
-Trial & Error
-Calculator
-Computer (Excel spreadsheet)
Here is a brief guide to do this using an MS Excel spreadsheet for this problem:
1) Select a column for the project's Cash flows (for example column "A").
2) Input the project's Cash Flows starting from the initial investment
(this is a negative input) and followed by the CF1 to CF4 cash flows,
each one in one cell of the column.
3) Click on the cell where you want your IRR calculated (say B1).
4) Enter "=IRR(" (without the quotes) and then highlight the column A
then close the parenthesis and hit enter.
For the project A the column A will have:
A1: -100,000
A2: 15,000
A3: 20,000
A4: 30,000
A5: 35,000
A6: 40,000
B1: =IRR(A1:A6)
You will find that IRR = 10.48% .
The correct answer is: c. 10.5%
Note that the IRR is lower than the cost of capital (13%), this is why
the NPV is negative and also indicates that this project is a bad
idea.
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3. How much should a $1,000-face-value bonds sell for, assuming the
following conditions:
The bond pays a coupon of 7%
The coupon payments are paid semi-annually.
The required rate of return on similar-risk investments is 7%.
The bond matures in 10 years
Remember that the value of a bond is the Present Value of all the
future payments (Coupons + Principal), the discount rate to calculate
this PV is i = 7%:
Coupon Payments = C = $1,000 * 0.07 / 2 = $35 (divided by 2 because
the coupons are paid in a semiannually rate)
The formula for the PV of the semiannually coupon payments is:
PV coupons = Coupon/(i/2) * [(1 - (1 / (1+i/2)^(2*10)))] =
= $35/0.035 * [(1 - (1 / (1.035)^20))] = (use a calculator here)
= $497.43
Now we must calculate the PV of the principal payment, for this semiannual bond is:
PV of principal = Face Value / (1+(i/2))^(2*10) =
= $1,000 / (1.035)^20 = (use a calculator here)
= $502.57
Bond value = PV coupons + PV of principal =
= $497.43 + $502.57 =
= $1,000
You can get from selling the bond $1,000 .As you have noted,the bond
price is the same that the face value, this is because the coupon rate
is similar to the required rate of return.
For reference on this topic see:
"4.2.2 - Basic bond valuation - Semiannual Interest":
http://www.wfu.edu/users/palmitar/Law&Valuation/chapter%204/4-2-2.htm#semiannualinterest
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I hope that this helps you. feel free to request for a clarification
if you need it before rate this answer.
Best regards,
livioflores-ga |