finance-P6-1 In this advanced problem, let’s look at the behavior of ordinary Treasury bonds

QUESTION

P6-1 In this advanced problem, let’s 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) ´ 2%

2

55.00

21.22

1,060.90

1,030.00(1.03) ´ 2%

3

55.00

21.85

1,092.73

1,060.90(1.03) ´ 2%

4

55.00

22.51

1,125.51

1,092.73(1.03) ´ 2%

5

1,055.00

1,182.46

1,159.27

1,125.51(1.03) ´ 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) ´ 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 bond’s 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) – 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) ´ 2%

2

55.00

21.42

1,071.20

1,030.00(1.04) ´ 2%

3

55.00

22.28

1,114.05

1,071.20(1.04) ´ 2%

4

55.00

23.17

1,158.61

1,114.05(1.04) ´ 2%

5

1,055.00

1,229.05

1,204.95

1,158.61(1.04) ´ 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) – Calculate your total dollar
return
1,000 x ($1.25 + $4) = $5,250

B) – Calculate your total
percentage return
($49 + $1.25 – $45) / $45 =
0.1167 or 11.67%

C) – Do the answers to parts (A) and (B) depend on whether you sell the
stock after one year of continue to hold it?
Answer doesn’t 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 ´ -0.2 + 0.65 ´ 0.18 + 0.2 ´ 0.4 = 0.167
Variance = 0.15 ´ (-0.2 – 0.167)2 + 0.65 ´ (0.18 – 0.167)2 + 0.2 ´ (0.4 – 0.167)2
=
.02020 + 0.00011 + 0.010858
=
.0311
Standard
deviation = .1765 or 17.65%

Stock
B:
Expected
return = 0.15 ´ -0.1 + 0.65 ´ 0.13 + 0.2 ´ 0.28 = 0.1255
Variance = 0.15 ´ (-0.1 – 0.1255)2 + 0.65 ´ (0.13 – 0.1255)2 + 0.2 ´ (.28 – 0.1255)2
= 0.00763 + 0.000013 +
0.004774
=
0.0124
Standard
deviation = 0.11

Stock
C:
Expected
return = 0.15 ´ –0.05 + 0.65 ´ 0.1 + 0.2 ´ 0.2 = 0.0975
Variance = 0.15 ´ (-0.05 – 0.0975)2 + 0.65 ´ (0.1 – 0.0975)2 + 0.2 ´ (0.2 – 0.0975)2
= 0.00326+ 0.000004 +
0.002101
=
0.005365
Standard
deviation = 0.073

 

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