Hi!!
1) Valuation Bond
Sadly, your great uncle Harry has passed way and has left you a GE
corporate bond in his will. This bond has a face value of
$1,000 and has an 8% annual coupon rate and will expire in 5 years
from today . You desire to cash this bond (sell) on the ?bond
market?. If the current interest rate required by investors for
similar investments is 7%, approximately how much
(in total ) will you realize from the sale of this bonds ?
( assume that you will receive 5 coupon payments)
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 * 0.08 = $80
For these bonds the formula for the present value of the 5 coupon
payments is the formula used to calculate the PV of a regular 5 years
annuity:
PV coupons = Coupon/I * [(1 - (1 / (1+I)^5))] =
= $80/0.07 * [(1 - (1 / (1.07)^5))] = (use a calculator here)
= $328.02
For reference on the formula see:
http://www.netmba.com/finance/time-value/annuity/
PV of principal = Face Value / (1+I)^5 =
= $1,000 / (1.07)^5 = (use a calculator here)
= $712.98
Bond value = PV coupons + PV of principal =
= $328.02 + $712.98 =
= $1,041
You can get from selling the bond $1,041 .
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2) Project Evaluation
Year cash flows
0 - 12000
1 + 4,000
2 + 5,000
3 + 6,000
4 + 1,000
A)Compute Payback
B)Compute NPV at 10%
C)Compute IRR using excel or interpolation
A) 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
The initial investment is $12,000 and you will recover it during the
third year, then:
Y = 2
and
U = $12,000 - ($4,000 + $5,000) = $3,000
PB = 2 + $3,000/$6,000 = 2.5 years
The payback period is 2 years and six months.
B) NPV:
Some definitions:
Present Value (PV):
CF1 CF2 CF3 CF4
PV = --------- + ---------- + ---------- + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4
Where r is the required return (10% or 0.1 in this case)
Net Present Value (NPV):
NPV = PV - I where I = Total Initial Investment
First calculate the PV of the cash flows:
PV = $4,000/1.1 + $5,000/(1.1)^2 + $6,000/(1.1)^3 + $1,000/(1.1)^4 =
= $3,636.36 + $4,132.23 + $4,507.89 + $683.01 =
= $12,959.50
NPV = PV - I = $12,959.50 - $12,000 = $959.5
The net present value of this project is $959.5
C) IRR:
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 CF3 CF4
PV = --------- + ---------- + ---------- + --------- = I
(1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4
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: -12,000
A2: 4,000
A3: 5,000
A4: 6,000
A5: 1,000
B1: =IRR(A1:A5)
You will find that IRR = 13.99% .
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I hope that this helps you, feel free to request for a clarification
if you need it.
Regards.
livioflores-ga |
