Hi!!
#1. NPV versus IRR
a. At what interest rates would you prefer project A to B?
Remember that:
Present Value (PV) for 3 years is:
CF1 CF2 CF3
PV = --------- + ---------- + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^3
and Net Present Value (NPV):
NPV = PV - I
You must use the NPV and PV formulas to build the following table:
Rate NPVA NPVB
0% $4,000.00 $5,000.00
2% $3,071.07 $3,558.06
4% $2,200.73 $2,224.91
4.11% $2,154.46 $2,154.54 ("No difference" rate)
6% $1,384.10 $990.48
8% $616.78 -$154.19
10% -$105.18 -$1,217.13
12% -$785.35 -$2,205.49
14% -$1,426.94 -$3,125.71
16% -$2,032.88 -$3,983.56
18% -$2,605.82 -$4,784.23
20% -$3,148.15 -$5,532.41
If the discount rate is 4.11% there is no difference between both
projects' NPVs (indiference point). Note that for rates greater than
4.11% the NPV of the project A is higher than the NPV of project B,
and for rates is lower than 4.11% the NPV of the project B is higher
than the NPV of project A. Since you must choice the project with
greater NPV you would prefer the project B if the interest rate is
below 4.11% and you would prefer project A if the interest rate is
above 4.11%.
(Note: I used an Excel spreadsheet to do the calculations and find the
indiference rate value by guessing -trying different values of rate in
the Excel spreadsheet's NPV formula until find the "no difference"
rate. I did that because there is no way to post a graph that shows
the intersection of both NPV profile, but you can use the above table
in an Excel spreadsheet and draw a graph to see such intersection)
----------------------------
b. What is the IRR of each project?
IRR is the discount rate r at which the NPV equals zero, in other
words it is the rate that satisfies:
NPV = PV - I = 0
Then IRR is the discount rate r at which:
PV = I
You can use different ways to calculate the IRR, for example:
-Trial & Error
-Calculator
-Computer (Excel spreadsheet)
I used an Excel spreadsheet for the calculations:
-Project A:
Column A : Column B
A1: -20,000 B1: =IRR(A1:A4)
A2: 8,000
A3: 8,000
A4: 8,000
IRR(A) = 9.70%
-Project B:
Column A : Column B
A1: -20,000 B1: =IRR(A1:A4)
A2: 0
A3: 0
A4: 25,000
IRR(B) = 7.72%
--------------------------------------------------------
#2. Project Evaluation
a. What is the initial investment in the product? Remember working capital.
The total initial investment (I) is the sum of the invest in plant and
equipment (in this case $50,000) plus the initial Working Capital
required (in this case is the 20% of the Revenues of Year 1 =
0.20*$40,000 = $8,000):
I = $50,000 + $8,000 = $58,000
-------------------------------
b. If the plant and equipment are depreciated over 4 years to a
salvage value of zero using straight-line depreciation, and the firm?s
tax rate is 40%, what are the project cash flows in each year?
For each year Yi (i = 1 to 4):
Depreciation = D = (Invest in plant and equipment) / 4 =
= $12,500
If we call Ri = revenues of Yi and Ei = expenses of Yi, then for each
year Taxes will be:
Ti = T * (Ri - Ei - D) with T = 0.4
Working Capital Change for year Yi:
ChWCi = Current WC - Previous Year WC
The cash flow formula states:
CF = Net Operating Profit - Taxes - Net Change in Working Capital
But note that for a given year i, (Ri - Ei) is the Net Operating Profit; then
we can say that in general:
CFi = Ri - Ei - T - ChWCi
Finally we have:
CF1 = 40,000 - 16,000 - 0.4*(11,500) - (-2,000) = $21,400
CF2 = 30,000 - 12,000 - 0.4*(5,500) - (-2,000) = $17,800
CF3 = 20,000 - 8,000 - 0.4*(-500) - (-2,000) = $14,200
CF4 = 10,000 - 4,000 - 0.4*(-6,500) - (-2,000) = $10,600
------------------------------
c. If the opportunity cost of capital is 10 percent, what is project NPV?
Present Value:
CF1 CF2 CF3 CF4
PV = --------- + ---------- + ---------- + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4
Net Present Value:
NPV = PV - I where I = Initial Investment
PV = $52,073.90
NPV = $52,073.90 - $58,000.00 =
= -$5,926.10
NEGATIVE NPV!! --->> you will lose money with this project.
-------------------------
d. What is project IRR?
IRR is the discount rate r that satisfies the following equation:
CF1 CF2 CF3 CF4
PV = --------- + ---------- + ---------- + --------- = I
(1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4
In other words IRR is the discount rate that makes the NPV equals to zero.
Use an Excel spreadsheet to calculate the IRR using the following inputs:
Column A values: Column B
A1: -58,000 B1: =IRR(A1:A5)
A2: 21,400
A3: 17,800
A4: 14,200
A5: 10,600
IRR = 4.59%
IRR lower than the opportunity cost of capital!! --->> you will lose
money with this project.
---------------------------------------------------------
#3 Calculating WACC
Let me call:
E = market value of equity
D = market value of debt
rE = cost of equity
rD = cost of debt
rP = premium
Tx = firm's tax rate
rW = overall required return (the WACC)
From the problem's statement we have:
E = book value of equity * price per share / book value per share =
= $10 million * $30 / $20 =
= $15 million
D = Bonds par value * rP =
= $5 million * 1.1 =
= $5.5 million
E+D = $20.5 million
rE = 0.15
rD = yield to maturity / rP =
= 0.09 / 1.1 =
= 0.0818
rP = 1.1
Tx = 0.4
The formula for the WACC is:
rW = (1-TX) * rD * D/(E+D) + rE * E/(E+D) =
= 0.6 * 0.0818 * 5.5/20.5 + 0.15 * 15/20.5 =
= 0.0132 + 0.1098 =
= 0.123 =
= 12.30%
See for reference:
"WACC - Weighted Average Cost of Capital":
http://www.valuebasedmanagement.net/methods_wacc.html
and
"PricewaterhouseCoopers WACC Formula":
http://www.pwcglobal.com/Extweb/pwcpublications.nsf/docid/2FC3C1F236E6ED328525694200135FB5
-----------------------------------------------------------
I hope that this helps you. Feel free to request for a clarification
if you need it.
Best regards.
livioflores-ga |
