## finance-P6-1 In this advanced problem, letâs look at the behavior of ordinary Treasury bonds

P6-1 In this advanced problem, letâs look at the behavior

of ordinary Treasury bonds and inflation-indexed bonds or TIPS as described in

the opening focus. We will simplify a little by assuming annual interest

payments rather than semiannual. Suppose over the next five years, investors

expect 3 percent inflation each year. The Treasury issues a five-year ordinary

bond that pays $55 interest each year. The Treasury issues a five-year TIPS

that pays a coupon rate of 2 percent. With TIPS, the coupon payment is

determined by multiplying the coupon rate times the inflation-adjusted

principal value. Like ordinary bonds, TIPS begin with a par value or principal

value of $1,000. However, that principal increases over time as inflation

occurs. Assuming that inflation is in fact equal to three percent in each of

the next five years, then the cash flows associated with each bond would look

like this:

Inflation-Indexed Bond (TIPS)

Year

T-Bond

Cash Paid

Inflation-Adjusted

Principal

Coupon Payment

Calculation

0 (cost)

-1,000.00

-1,000.00

-1,000.00

NA

1

55.00

20.60

1,030.00

1,000.00(1.03) Â´ 2%

2

55.00

21.22

1,060.90

1,030.00(1.03) Â´ 2%

3

55.00

21.85

1,092.73

1,060.90(1.03) Â´ 2%

4

55.00

22.51

1,125.51

1,092.73(1.03) Â´ 2%

5

1,055.00

1,182.46

1,159.27

1,125.51(1.03) Â´ 2%

Notice in

the last row of the table the final TIPS payment includes the return of the

inflation-adjusted principal ($1,159.27) plus the final coupon payment.

a. Calculate the

yield to maturity of each bond. Why is one higher than the other? Show that the

TIPS YTM equals the product of the real interest rate and the inflation rate.

b. What is the real

return on the T-bond?

c. Suppose the

real return on the T-bond stays constant, but investors expect four percent

inflation rather than three percent. What happens to the required return on the

T-bond in nominal terms?

d. Imagine that

during the first year, the inflation that actually occurred was three percent

as expected. However, suppose that by the end of the first year, investors had

come to expect four percent inflation for the next four years. Fill out the

remaining cash flows for each bond in the table below.

Inflation-Indexed Bond (TIPS)

Year

T-Bond

Cash Paid

Inflation-Adjusted

Principal

Coupon Payment

Calculation

0 (cost)

-1,000.00

-1,000.00

-1,000.00

NA

1

55.00

20.60

1,030.00

1,000.00(1.03) Â´ 2%

2

3

4

5

e. Now calculate

the market price of the Treasury bond as of the end of the first year. Remember

to discount the bondâs remaining cash flows using the nominal required return

that you calculated in part c. Given this new market price, what is the total

return offered by the T-bond the first year?

f. Next, calculate

the market price of the TIPS bond. Remember, at the end of the first year, the

YTM on the TIPS will equal the product of one plus the real return (2%) and one

plus the inflation rate (4%). What is

the total return offered by TIPS the first year?

A6-1. a. The

YTM of the T-bond is 5.5% and the YTM of the TIPS is 5.06%. (Note that the YTM

for the TIPS is the IRR of the cash paid column.) Another way of looking at TIPS yield is:

(1.02)(1.03) â 1 = 0.0506. The T-bond

offers a higher yield because it does not enjoy protection from inflation risk

as the TIPS bond does. An investor who buys a T-bond must receive compensation

for bearing this risk, while a TIPS investor does not require compensation for

inflation risk.

b. The real return on the T-bond is found by

solving this equation: (1+0.055) = (1 + 0.03)(1 + x). Solving we find that x =

2.43%. This is approximately equal to the nominal rate, 5.5%, minus the

inflation rate, 3%. Notice that the real rate offered by the T-bond is higher

than the 2% real rate offered by TIPS. The reason is given in part a.

c. The required return on the T-bond if inflation

expectations go up is 6.53% which is found by solving for x in this

equation: (1 + x) = (1 + 0.04)(1 +

0.0243).

d. The missing values are filled in below:

Inflation-Indexed Bond (TIPS)

Year

T-Bond

Cash Paid

Inflation-Adjusted

Principal

Coupon Payment

Calculation

0 (cost)

-1,000.00

-1,000.00

-1,000.00

NA

1

55.00

20.60

1,030.00

1,000.00(1.03) Â´ 2%

2

55.00

21.42

1,071.20

1,030.00(1.04) Â´ 2%

3

55.00

22.28

1,114.05

1,071.20(1.04) Â´ 2%

4

55.00

23.17

1,158.61

1,114.05(1.04) Â´ 2%

5

1,055.00

1,229.05

1,204.95

1,158.61(1.04) Â´ 2%

e. The market price of the Treasury equals $964.74. This is

found by discounting four more years of $55 coupons plus the principal at a

nominal rate of 6.53%.

(Calculator inputs: N = 4, PMT = 55, I = 6.53%, FV = 1,000 and solve for PV =

-$964.74). The total return of this bond

the first year is $19.74 or 1.974%.

Return is (55 + 1,000-964.74)/1,000 = 1.974%

f. To calculate the market price of TIPS, you first have to

calculate the nominal interest rate used to discount cash flows. Solve for

x: (1 + x) = (1.02)(1.04) so x = 0.0608

or 6.08%. Now discount the cash flows over the last four years as determined in

part (d) at this rate and you get the price of TIPS, $1,030. In other words,

the price of the TIPS bond is currently equal to its inflation-adjusted par

value. The total return on TIPS the first year is ($1,030 + $20.60 – $1,000)

$50.60 or 5.06%, exactly the YTM calculated in part (a). In this problem, interest rates changed because

inflation rose. The increase in inflation did not affect the first-year return

on TIPS, but it did affect the first-year return on T-bonds.

P6-2 You purchase

1,000 shares of Spears Grinders, Inc. stock for $45 per share. A year later, the stock pays a dividend of

$1.25 per share and it sells for $49.

A) â Calculate your total dollar

return

1,000 x ($1.25 + $4) = $5,250

B) â Calculate your total

percentage return

($49 + $1.25 – $45) / $45 =

0.1167 or 11.67%

C) â Do the answers to parts (A) and (B) depend on whether you sell the

stock after one year of continue to hold it?

Answer doesnât depend on if you

should sell the stock or hold it

P7-1. Calculate the

expected return, variance, and standard deviation for the stocks in the table

below.

Product Demand

Probability

Stock #1

Stock #2

Stock #3

High

20%

30%

20%

15%

Medium

60%

12%

14%

10%

Low

20%

-10%

-5%

-2%

A7-1. Expected returns are: Stock 1 (11.2%);

Stock 2 (11.4%); Stock 3 (8.6%)

Variances are: Stock 1 (160.96); Stock 2 (69.9); Stock 3 (31.1)

Standard deviations are: Stock 1 (12.7%); Stock 2 (8.4%); Stock 3 (5.6%)

P7-2. Calculate the expected return,

variance, and standard deviation for each stock listed below.

State of the

Economy

Probability

Stock A

Stock B

Stock C

Recession

15%

-20%

-10%

-5%

Normal growth

65%

18%

13%

10%

Boom

20%

40%

28%

20%

A7-2. Stock A:

Expected

return = 0.15 Â´ -0.2 + 0.65 Â´ 0.18 + 0.2 Â´ 0.4 = 0.167

Variance = 0.15 Â´ (-0.2 â 0.167)2 + 0.65 Â´ (0.18 â 0.167)2 + 0.2 Â´ (0.4 â 0.167)2

=

.02020 + 0.00011 + 0.010858

=

.0311

Standard

deviation = .1765 or 17.65%

Stock

B:

Expected

return = 0.15 Â´ -0.1 + 0.65 Â´ 0.13 + 0.2 Â´ 0.28 = 0.1255

Variance = 0.15 Â´ (-0.1 â 0.1255)2 + 0.65 Â´ (0.13 â 0.1255)2 + 0.2 Â´ (.28 â 0.1255)2

= 0.00763 + 0.000013 +

0.004774

=

0.0124

Standard

deviation = 0.11

Stock

C:

Expected

return = 0.15 Â´ â0.05 + 0.65 Â´ 0.1 + 0.2 Â´ 0.2 = 0.0975

Variance = 0.15 Â´ (-0.05 â 0.0975)2 + 0.65 Â´ (0.1 â 0.0975)2 + 0.2 Â´ (0.2 â 0.0975)2

= 0.00326+ 0.000004 +

0.002101

=

0.005365

Standard

deviation = 0.073

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