Valuation of bonds and shares

SOLUTIONS TO PROBLEMS

10-1*

or 1000 +/- FV 80 +/- PMT 12 N 12 I/Y COMP PV giving $752.23 or using APPENDIX D, using APPENDIX B,

Total Present Value ≈ 495.52 + 257.00 ≈ $752.52

10-3*

Semi-annual coupon payments:

or 1000 +/- FV 45 +/- PMT 16 N 4 I/Y COMP PV giving $1,058.26 or using APPENDIX D, using APPENDIX B,

Total Present Value ≈ 524.34 + 534.00 ≈ $1,058.34

Annual coupon payments:

or 1000 +/- FV 90 +/- PMT 8 N 8 I/Y COMP PV giving $1,057.47 or using APPENDIX D, using APPENDIX B,

Total Present Value ≈ 517.23 + 540.00 ≈ $1,057.23

10-5*

10-7*

10-9*

10-11*

(a)

(b)

10-13*

10-15*

We need to solve for Rb, either by trial and error or using a financial calculator.

1000 +/- FV 90 +/- PMT 20 N 945 PV COMP I/Y giving 9.63%

10-17*

(a)

We need to solve for Rb, either by trial and error or using a financial calculator.

1000 +/- FV 80 +/- PMT 15 N 1085 PV COMP I/Y giving 7.06%

(b)

or 1000 +/- FV 80 +/- PMT 15 N 10 I/Y COMP PV giving $847.77 or using APPENDIX D, using APPENDIX B,

Total Present Value ≈ 608.48 + 239.00 ≈ $847.48

(c)

Since the expected rate of return (7.06%) is less than your required rate of return of 10%, the bond is not an acceptable investment. This fact is also evident because the market price ($1,085) exceeds the value of the security to the investor ($847.48).

10-19*

(a)

(b)

(c)

Yes, the investment should be undertaken, as the expected rate of return (14.07%) is greater than your required rate of return (10.5%). Also, your value of the shares ($57.02) exceeds the current market price ($23.50).

10-21*

We need to solve for Rb, either by trial and error or using a financial calculator.

1000 +/- FV 90 +/- PMT 15 N 1250 PV COMP I/Y giving 6.36%

10-23*

(a)

(b)

(c)

The investor should purchase the preference share because:

The price the investor is prepared to pay of $36 is more than the current price of the share in market of $33.

The return the investor requires of 10% is less than the 10.91% return that can be expected from investing in the share.

SOLUTIONS TO PROBLEMS – APPENDIX TO CHAPTER 10

A-1

PVDG model:

Constant growth dividend model:

A-2

(a)

(b)

The share prices for each scenario are shown in the table below. The calculations for the first price in the second column (ROE = 16%, Retention rate = 30%) are:

Retention rate

Possible ROE

0%

30%

60%

16%

$38.89

$37.12

$33.33

18%

$38.89

$38.89

$38.89

24%

$38.89

$45.37

$77.78

(c)

Our results show that value is created only when management reinvests at above the investor’s required rate of return. That is, growth may actually decrease the firm’s value if the profitability of the new investment is not sufficient to satisfy the investor’s required rate of return.

SOLUTIONS TO CONCEPT CHECK QUESTIONS

10.1 If the intrinsic value is greater than the market value, then in the eyes of the investor the asset is undervalued and would be good to buy. On the other hand, if the market value is less than the intrinsic value, the asset is overvalued and should not be purchased, or if the investor already owns the asset it should be sold. It is essential that market value equals intrinsic value so that securities are fairly priced and, in doing so, this indicates that the market is operating efficiently.

10.2 Risk helps determine what correct required rate of return (discount) is applicable to a particular security to induce an investor to invest in that security. For example, the higher the risk or beta, the higher rate of return is required as an inducement to invest.

10.3

Element 1: The risk-return trade-off – we won’t take on additional risk unless we expect to be compensated with additional return.

Element 2: The time value of money – a dollar received today is worth more than a dollar received in the future.

Element 3: Cash – not profits – is king.

10.4 Some of the important