Accounting

Problem Set II

Problem P9 - 17:

FV (Table 1) at 11% discount rate

2.00 x .901 = $1.80

2.20 x .802 = $1.79

2.40 x .731 = $1.75

33.00 x .731 = $24.12

--------

$29.46

Problem P9 - 22:

Alternative Present Values: Your rich godfather has offered you a choice of one of the three following alternatives: $10,000 now; $2,000 a year for eight years; or $24,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?

Solution:

(first alternative) Present value of 10,000 received now: 10,000

(second alternative) Present Value of annuity of 2,000 for eight years:

Appendix D

PVa=AxPVifa

=2,000xPVifa (11%,8years)

=2,000x5.146

=10,292

(third alternative) Present value of 24,000 received in 8 years

Appendix B

PV= FV x PVif

=24,000 x PVif(11%, 8 years)

I would select 24,000 to be received in 8 years

Revised answer based on 12%

First alternative present values of 10,000 received today 10,000

Second - present value of annuity of 2,000 for 8 years (same as above but use 12)

Problem P9 - 23

Payments Required: You need $28,974 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.

a. What single payment could be made at the beginning of the first year to achieve this objective?

Appendix b

PV=FV X PVif(8%, 10 periods)

=28,974 x .463 = 13,415

b. What amount could you pay at the end of each year annually for 10 years to achieve this same objective?

Appendix C

A=FVA/FV(IFA) = 28,974/14.487= $2,000

Problem P10 - 2:

2. Midland Oil has $1000 par value bonds outstanding at 8 percent interest. The bonds will mature in 25 years. Compute the current price of the bonds if the present yield to maturity is:

7 Percent

PVa = A x PV (n=25, i=7%)

PV = 80 x 11.654

= 932.32

PV = FV x PV (n=25, i =7%)

PV = 1000 x .184

= $184

Present value of interest payments $932.32

Present value of principal payment a maturity 184.00

Price of the bond $ 1,116.32

10 Percent

PVa = A x PV (n=25, i=10%)

PV = 80 x 9.077

= 726.16

PV = FV x PV (n=50, i =10%)

PV = 1000 x ..092

= 92$

Present value of interest payments $726.16

Present value of principal payment a maturity 92.00

Price of the bond $ 818.16

13 Percent

PVa = A x PV (n=25, i=13%)

PV =

PV = FV x PV (n=25, i =13%)

PV = 1000 x .002

= 2

Present value of interest payments $997.75

Present value of principal payment a maturity 2.00

Price of the bond $ 999.75

Problem P10 - 7:

Go to Table 10-1 which is based on bonds paying 10 percent interest for

20 years. Assume interest rates in the market (yield to maturity) decline from

11 percent to 8 percent:

a. What is the bond price at 11 percent? 920.30

b. What is the bond price at 8 percent? 1,196.80

c. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent?

920.30 - 1196.80 = -276.5

276.5 / 920.30 * 100 = 30 %

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