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Lecture 6

MGFC10H3 Lecture Notes - Lecture 6: Net Present Value

2 pages124 viewsFall 2013

Department
Management
Course Code
MGFC10H3
Professor
Sultan Ahmed
Lecture
6

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Given E1 = $5, D1 = $3, b = 0.4, k = 0.15, and g = 0.08. [In this example, we assume the
constant growth model, that means the firm has constant growth opportunities in every
year.]
What is ROE? ROE = g/b = 0.08/0.4 = 0.2
Value of the firm if no growth =
33.33$
15.0
5
.
Value of the firm with growth =
86.42$
08.015.0
3
.
Then NPVGO = $42.86 $33.33 = $9.52
Or we can calculate NPVGO directly. Let’s look at the time line below:
Period ………
………
1st growth opportunity
………
2nd growth opportunity ………
3rd growth opportunity ………
4th growth opportunity ………
5th growth opportunity ………
-2.720978
0.46656
0.503885
-2.519424
0.4
0.432
-2.3328
0.432
0.46656
0.432
3
-2
0.4
0.4
0.4
-2.16
5
5
5
5
5
0
5
1
4
2
At the end of year 1, the firm reinvests 40% ($2) of its earnings and this investment will
generate a profit of $0.4 ($2*0.2) per year in years 2, 3, 4, …….( Since ROE = 20%).
*D1 = $5 $2 = $3
Therefore, the total earnings = $5.4 in year 2. As the firm keeps the same payout ratio, it
reinvests $2.16 ($5.4*0.4) in year 2. This second GO will generate earnings of $0.432
($2.16*0.2) per year forever.
*D2 = $5.4 $2.16 = $3.24 (= $3*1.08)
So the total earnings in year 3 = $5.832, reinvests $2.3328 ($5.832*0.4) and earns
$0.46656 per year forever.
*D3 = $5.832 $2.3328 = $3.4992 (=$3*1.08*1.08)
You can calculate the same for year 4, year 5, year 6, …….
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