Discounting versus Capitalizing
1. b
2. c
3. a
4. b
a. The midyear convention always produces a higher value because it assumes that the cash flows are received earlier and therefore need to be discounted for a shorter time period.
9. Gordon Growth Model 10. (also residual value)
11. |
$10 0.08 |
= $125 |
|
12. |
c = |
k- o |
|
c = |
0.10 -0.06 |
0.04 |
|
13. |
PV = |
$1.00(1 |
+ 0.05) |
0.12- |
-0.05 |
||
$1.05 |
|||
0.07 |
|||
= $15 |
PV =
$1000 $1200 $1400 $1550 $1700 (1700x1.06) /(0.20- 0.06)
1.20 (1.20)2 (1.20)3 (1.20)4 (1.20)5 (1.20)5
$1000 $1200 $1400 $1550 $1700 $1802/0.14
1.20 1.44 1.73 2.07 2.49 2.49
= $833.33+ $833.33+ $809.25+ $748.79 + $682.73+ $5,169.25 = $9,076.68
This also be set up as factors:
Year 1: Year 2: Year 3: Year 4: Year 5:
|
]/1.20 = 0.8333 x $1,000 1/1.44 = 0.6944 x $1,200 1/1.73 = 0.5780 x $1,400
1/2.07 = 0.4831 x $1,550 1/2.49 = 0.4016 x $1,700
1/2.49 = 0.4016 x $12,871
(Differences are due to rounding.) ..00(1 + 0.05)(1 + 0.12)5
PV =
0.12-0.05 _ $1.05(1.06)
0.07 _ 1.11 ~ 0.07 = $15.86
$833.00 $833.28 $809.20 $748.81 $682.72 55,168.9.9 59.076.00
PV = |
$1000 $1200 $1400 $1550 $1700 $1700(1.06)(1.20)a5 / (0.20- 0.06)
(1.20)a $1000 1.10 |
(1,20)5 |
2.49 $5,656.91 |
(1.20)1'5 (1.20)" (1,20)3'5 (1,20)45 $1200 $1400 $1550 $1700 $1700(1.16)/0.14
1.31 1.58 1.89 2.27 $916.03 + $886.08 + $820.11
= $9,937.12 This also could be set up as factors:
).10 $916.08 $886.06 $820.11 $748.85 5.94 |
1/1.10 = 0.9091 x $1,000 1/1.31= 0.7634 x $1,200 0.6329 x $1,400 0.5291 x $1,550 0.4405 x $1,700 0.4016 x $14,086 |
1/1.58 1/1.89 1/2.27 1/2.49 |
ear
Year 3: Year 4: Year 5:
$9,937.14 |
This could be calculated as
$1000 $1200 $1400
$1550 $1700 $1700(1.06)/(0.20-0.06)
(1.20)'
(1.20)05 (1.20)15 (1.20f5 (1.20f5 (1.20r5 _ $1000 $1200 $1400 $1550 $1700 $1802/0.14
1.10 1.31 1.58 1.89 2.27 2.27
= $909.09 + $916.03 + $886.08 + $820.11 + $748.90 + $5,670.23 = $9,950.44
Set up in terms of factors, it would look as follows:
1/1.10 = 0.9091 x $1,000 1/1.31 = 0.7634 x $1,200 1/1.58 = 0.6329 x $1,400 1/1.89 = 0.5291 x $1,550 1/2.27 = 0.4405 x $1,700 1/2.27 = 0.4405 x $12,871 |
Year 1
Year 2
Year 3
Year 4
Year 5
Differences are due to rounding:
$909.10 $916.08 $886.06 $820.11
35,669.68 39,949.88
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