ChAF208 CORPORATE FINANCE06 2e PDF

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6.5

What is the intrinsic value of a security and why do we focus on intrinsic values in finance?

The intrinsic value of a security is the present value of expected future cash flows. Cash flows are forecast and then discounted at the investor’s required return. Intrinsic value is the appropriate value for finance because it applies the principles of the time value of money. 6.6

Describe the variables that are used to determine a security’s intrinsic value and explain the role of each variable.

The basic security valuation equation is: n

V =∑

CF t

t t =1 (1+r ) It states that the intrinsic value of a security is a function of the size and timing of the cash flows that will be generated by the security. The cash flows are discounted to reflect the time value of money. The discount rate used is the investor’s required return. If the security can be purchased for less than its intrinsic value, the investor will earn more than his required return.

6.10 What is a zero coupon bond? Is the calculation of the intrinsic value of a zero coupon bond different from that for a coupon bond? Explain. A zero coupon bond does not have any coupon payments over its term to maturity. This means that interest is paid via the difference between the purchase price and the maturity value of the bond. Coupon bonds do receive regular interest payments over their lives plus the payment of face value at maturity. The implication for valuation is that the intrinsic value of a zero coupon bond is the PV of its face value. The intrinsic value of a coupon bond, on the other hand, is the present value of the face value plus the present value of the coupon payments over the bond’s life.

6.12

If dividends are paid semi-annually on a preference share and we adjust the required return to reflect this, is the intrinsic value any different to a share with the same total dividend paid annually and an annual required return? Use an annual dividend of $1 and a required return of 9% to demonstrate your understanding.

The cash flows of a preference share form a perpetuity. As shown by the following calculations, there is no difference in the intrinsic value of a preference share paying and annual dividend of $1 compared to a semiannual dividend of $0.50 for a given investor. 1 0 .50 V p= V p= =$ 11. 11 =$ 11. 11 0 .09 0 .045

Introducing Corporate Finance 2e Solution Manual

If we were looking at a security with a finite life, we would find that the security with more frequent cash inflows would have a higher intrinsic value. 6.20

Is there a theoretical relationship between the constant growth model and the PE method of valuation? What does the relationship depend on?

The theoretical relationship between the constant growth model and the PE method of valuation is that both will give the same valuation for a share when you use the same assumptions in your forecasts of dividends and earnings.

Financial Problems 6.1

You have been offered an investment with the following cash flows: End year $ 1 50 2 80 3 300 If you have a discount rate of 7% p.a., how much is this investment worth to you? n

V =∑ t−1

CF t (1+ r )n

50 80 300 V= + + 1 2 ( 1+0 .07) ( 1+0 .07 ) ( 1+0 .07 )3 V =46 .73+69. 88+244 . 89=$ 361 . 49 6.4

Zed Ltd zero coupon bonds have a face value of $500 000 and 2 years to maturity. Your nominal required return is 7% p.a., compounded semiannually. What is the intrinsic value of the bond?

V b=

500 , 000

(1+ 0 .072 )

=

2∗2

500 , 000 1 .1475

= $435 729.80

6.6

Crown Ltd bonds have 4 years to maturity, coupons of 9.5% and a face value of $100. Coupons are paid semi-annually. If your required return is 8% p.a., what is the intrinsic value of a Crown bond?

Chapter 6: Valuation of bonds and shares

n

V b =∑

t =1

Using equation 6.4

Ct =

0 . 095 ×100=4 . 75 2

Ct

(1+r b )t

rb=

+

F n 1+ ( rb )

0 .08 =0 .04 2

As the stream of coupon payments forms an annuity with a term of 8 periods and a discount rate of 4%: V b =C

[

]

1−( 1+ r b )−n F + rb ( 1+r b )n

=4 .75

[

]

1−(1+0 .04 )−8 100 + 0. 04 (1+0 .04 )8

= 4.75 (6.7327) + 100 (1.3686) = 31.98 + 73.07 = $105.05

6.7

Ct =

Vision Systems bonds have a face value of $500 000, a coupon of 7.75% and 7 years to maturity. Coupons are paid semi-annually. If your required return is 11% p.a., what is the intrinsic value of this bond?

0 . 0775 ×500 , 000=19 , 375 2 V b =C

[

]

rb=

0 .11 =0 .055 2

1−(1+ r b )−n F + rb ( 1+r b )n

[

]

1−( 1+0 . 055 )−14 500 , 000 + 0. 055 (1+0 . 055)14 500000 =19375 ×9 .5897+ 2 .1161 = 185 799.43 + 236 283.73 = $422 083.16 =19 , 375

6.14

XYZ pays semi-annual dividends. The last dividend was 50c and was paid yesterday. Your forecast growth rate is 3% p.a. Forecast the dividends for the next 4 years.

D1 = D0(1 + g) = 0.50(1 + 0.015) = 0.5075 D2 = D0(1+g)2 = 0.50 (1 + 0.015)2 = 0.5151

Introducing Corporate Finance 2e Solution Manual

D3 = D0(1+g)3 = 0.50 (1 + 0.015)3 = 0.5228 D4 = D0(1+g)4 = 0.50 (1 + 0.015)4 = 0.5307 D5 = D0(1+g)5 = 0.50 (1 + 0.015)5 = 0.5386 D6 = D0(1+g)6 = 0.50 (1 + 0.015)6 = 0.5467 D7 = D0(1+g)7 = 0.50 (1 + 0.015)7 = 0.5549 D8 = D0(1+g)8 = 0.50 (1 + 0.015)8 = 0.5633

6.15

You are considering the purchase of some shares. The shares pay semiannual dividends and you have forecast the next four dividends to be 20c, 22c, 28c and 31c. You expect to sell the share for $6.75 right after you receive the fourth dividend. If your required return is 12% p.a., what is the value of the share? n

V e=∑ t −1

Dt

Pn + ( 1+ r b ) (1+r e )n

0 .22 0 . 28 0. 20 + + 0 . 12 1 0. 12 2 0 .12 1+ 1+ 1+ 2 2 2 V e= 0. 19+ 0 . 20+0 . 24 + 5 .59 = $ 6 .22 V e=

(

6.16

) (

) (

+

0 .31+6 . 75 0. 12 4 1+ 2

) ( 3

)

As part of your retirement funding strategy, you are considering the purchase of ordinary shares in Australian Ethical Investments Ltd. Dividends are paid semi-annually and you have forecast the next six. The first of these dividends will be received in 6 months’ time. Dividend

Chapter 6: Valuation of bonds and shares

You are planning to sell the shares when you have received the final dividend and you expect to get $14 for each share. If your required rate of return is 6% p.a., what is the intrinsic value of a share? n

V e=∑

Dt t

+

Pn n

t=1 ( ( s) s) Using equation 6.6 D2 D3 D4 D5 D1 D +P + + + + V e= + 6 66 1 2 3 4 5 (1+r ) ( 1+r ) ( 1+r ) ( 1+r ) ( 1. 04 ) ( 1 .04 )

=

1+ r

1+r

0 . 27 0 .32 0. 35+14 0. 20 0. 30 0 .20 + + + + + 1 3 2 4 (1 .03 ) (1. 03 ) (1. 03 ) (1 . 03 ) (1. 03 )5 (1 . 03)6

= 0.1942 + 0.1885 + 0.2471 + 0.2665 + 0.2760 + 12.0174 = $13.19

6.17

Calliope Ltd has been listed for the last 20 years. Over this time, investors have enjoyed a steady stream of dividends. You expect the current annual growth rate of about 1% to be maintained into the foreseeable future. Dividends are paid semi-annually and the dividend paid last week was 13c per share. If your required return for Calliope is 5% p.a., what is the intrinsic value of a share?

Using equation 6.7 D(1+g ) V e= r e−g 0 .13 (1+0. 005 ) = 0 .025 −0 . 005

V e=

D1 r e−g

The last dividend would have been a semi-annual one. The growth rate and required return, however, are annual so need to be divided by two.

=

6.18

V e=

0 .13065 0 . 02

= $6.53

You have forecast an annual growth rate of 3% for MOP Ltd. Dividends are paid annually and the last dividend was 50c. If your required return is 12% p.a., what is the value of an MOP share?

D1 r e−g

V e=

0 . 50(1+0 .03 ) =$ 5. 72 0 . 12−0 . 03

Introducing Corporate Finance 2e Solution Manual

6.19

V e=

You have forecast the next annual dividend of Topboy Ltd at $1. You expect that the following dividends show a 5% increase for each of the next 2 years. After that, you forecast a growth rate of 1% p.a. and expect this growth to continue indefinitely. If your required return is 10% p.a., what is the value of a Topboy share?

D1

( 1+r e )

1

+

D2

+

D3

(1+r e ) (1+r e ) 2

3

+

D4 1+r e )−n r e −g (

1(1+0. 05 ) 1 ( 1 +0 . 05)2 1 (1 +0. 05 )2 (1+0 . 01) 1 + ( 1+0 .10 )−3 + + 0 .10−0 .01 (1 +0. 10 )1 (1+0 .10) 2 (1+0 . 1)3 V e= 0. 9091+ 0 . 8678 + 0 . 8283 + 9 . 2956= $ 11. 90 V e=

6.20 Shares in Cochlear Ltd have been trading on the ASX for about 12 years. Over that time, the company has experienced a phenomenal growth rate in dividends of about 25% p.a. This growth has been achieved by expanding into overseas markets and, to a lesser extent, by new product development. You expect that growth in US sales will support the current growth in dividends for a further 5 years. After that time, you expect dividend growth to slow to about 10% p.a. and the new growth rate to be maintained for many years to come. Total dividends last year were 51 cents. The next dividend payment is due 6 months from now and dividends are paid semi-annually. What is the intrinsic value of a Cochlear share if your required rate of return is 16% p.a.? V e=

D( 1+ g1 ) D( 1+ g1 )2 D( 1+ g 1 )10 D( 1+ g1 )10 ( 1+ g2 ) 1 × + + +.. .. .+ 2 r e−g ( 1+ r e ) ( 1+r e )10 ( 1+ r e ) ( 1+ r e )10

=

=

0 .255 (1+0. 125 ) 0 .255 (1+0. 125)2 0 . 255(1+0 . 125)10 0 . 255 (1+ 0 .125 )10 (1+0. 05 ) 1 + +. . .. .+ + × (1+0 .08 ) 0 .08−0 . 05 (1+0. 08 )2 (1+0 . 08 )10 (1+0. 08 )10

(

0 .2869 0 .3227 0 .3631 0. 4085 0 . 4595 0 .517 0. 5816 0. 6543 0 . 7361 0 . 8281 0 .86947 1 + + + + + + + + + + 1. 08 1. 1664 1. 2597 1. 3605 1. 4693 1 .5869 1. 7138 1. 8509 1 . 999 2 .1589 . 03 2 .1589

)

= 0.2656 + 0.2767 + 0.2882 + 0.3003 + 0.3127 + 0.3258 + 0.3393 + 0.3535 + 0.3682 + 0.3836 + 13.4244 = $16.64

6.27 (a) The last dividend on an ordinary share was $0.50. You expect the dividends to grow at 2% per annum for the foreseeable future. What is the value of the share if the required return is 10% p.a.?

V e=

D1 r e−g V e=

0 . 50(1+0 .02 ) =$ 6. 38 0 . 10−0 . 02

(b) The next dividend on an ordinary share is expected to be $0.50. You expect the dividends to grow at 2% per annum for the foreseeable future. What is the value of the share if the required return is 10% p.a.?

V e=

0 .50 =$ 6 .25 0 . 10−0 . 02...