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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