10/8/12
Problem Set 2
Inflation & the Yield Curve
Problem 1
•  Real rate in Germany:
(4% – 1%) / 1.01 = 2.97%
•  Real rate in United States:
(3% – 2%) / 1.02 = 0.98%
Money will flow to the higher real rate, flowing from
the U.S. into Germany
Pressures will be on The U.S. nominal rate to rise
The German nominal rate to decline
1
10/8/12
Problem 2
•  Real rate in Japan:
(5% – 1%) / 1.01 = 3.96%
•  Real rate in UK:
(4% – 3%) / 1.03 = 0.97%
Money will flow to the higher real rate, flowing from
the UK into Japan
Pressures will be on The UK nominal rate to rise
The Japanese nominal rate to decline
Problem 3
•  R = r + i + ri
•  R = .03 + .04 + (.03 * .04) = 7.12%
2
10/8/12
Problem 4
Two-year bond
R = 6.5%
P/YR = 1
N=2
Let’s say PV = $10,000
Then FV = $11,342.25
Rollover Strategy
Start with $10,000
1st year add 6%
$10,600
2nd year add 7.5%
$11,395
2-year average return is 6.75%
Expected return is higher with rollover strategy
What risks are involved?
Problem 5/6
Two-year bond
R = 7%
P/YR = 1
N=2
Let’s say PV = $10,000
Then FV = $11,449.00
Rollover Strategy
Start with $10,000
1st year add 6%
$10,600
2nd year add 7.5%
$11,395
2-year average return is 6.75%
Expected return is higher with two-year bond
What pressures would result?
Given the expectations, equilibrium 2-year rate would be
6.75% (Problem 42)
3
10/8/12
Problem 7
Start with $1000
Average return:
PV is –1000
FV is 1190.91
P/YR is 1
N is 3
Calculate interest
Result is 6.00 %
1st year add 5%
$1050
2nd year add 6%
$1113
3rd year add 7%
$1190.91
Problem 8
Start with $1,000,000
1st year add 6%
$1,060,000
2nd year add 6.5%
$1,128,900
3rd year add 7%
$1,207,923
4th year add 8%
$1,304,556.84
Average return:
PV is –1,000,000
FV is 1,304,556.84
P/YR is 1
N is 4
Calculate interest
Result is 6.8724 %
4
10/8/12
Problem 9
•
•
•
•
•
PV = –0.58
FV = 1
P/YR = 1
N = 9
Compute I/YR
•  Result: 6.24%
Problem 10
•
•
•
•
•
PV = –1
FV = 4
P/YR = 1
N=20
Compute I/YR
•  Result: 7.18%
5
10/8/12
Problem 11
•
•
•
•
•
PV = –1
FV = 32
P/YR = 1
N = 100
Compute I/YR
•  Result: 3.53%
Problem 12
•
•
•
•
•
PV = –32
I/YR = 3.53%
P/YR = 1
N = 100
Compute FV
•  Result: $1,024
6
10/8/12
Problem 13
•
•
•
•
•
PV = –1
I/YR = 10%
P/YR = 1
N = 1
Compute FV
•  Result: 90.91¢
Problem 14
•
•
•
•
•
PV = –1
I/YR = 10%
P/YR = 1
N = 10
Compute FV
•  Result: 38.55¢
7
10/8/12
Fisher Effect: R = r + i + ri
•  Prob 15: r = 3%
i = 5% R = 8.15%
FV = $1000, PV = $924.64
•  Prob 16: r = 3%
i = 5% R = 8.15%
Prob 17: FV = $1000, PV = $456.81
•  Prob 18: r = 3%
i = 4% R = 7.12%
FV = $1000, PV = $933.53
•  Prob 19: r = 4%
i = 3% R = 7.12%
•  Prob 20: FV = $1000, PV = $502.68
Fisher Effect: r = (R – i)/(1+i)
•  Prob 21: R = 9%
i = 3% r = 5.83%
PV = –100,000; FV = $411,843.13
•  Prob 22: R = 3%
i = 4% r = 5.83%
PV = –100,000; FV = $74,837.03
•  Prob 23: R = 12%
i = 3% r = 8.74%
PV = –100,000; FV = $534,091.86
•  Prob 24: R = 12%
i = 3% r = 8.74% 8
10/8/12
Problem 25: Artwork Purchase
•  Purchase price in 1977 was $300,000
•  Selling price in 2007 was $1,250,000
Step 1: Adjust selling price for inflation
•  I/YR = 6%
•  P/YR = 1
•  N = 30
•  FV = 1,250,000
•  Compute PV
•  Result: $217,637.66
Then input this as FV, set PV to –300,000, and compute I/YR
•  Result: –1.06%
Problem 26: Home Purchase
•  Purchase price in 1997 was $200,000
•  Selling price in 2007 was $350,000
Step 1: Adjust selling price for inflation
•  I/YR = 4%
•  P/YR = 1
•  N = 10
•  FV = 350,000
•  Compute PV
•  Result: $236,447.46
Then input this as FV, set PV to –200,000, and compute I/YR
•  Result: 1.69%
9
10/8/12
Real return after tax: r = (R(1–t) – i)/(1+i)
•  Prob 27: R=4% t=35% i=3% r = –0.39%
•  Prob 27: R=6.9% t=35% i=5% r = –0.49%
Problem 29
•
•
•
•
•
•
•
•
•
Desired income $3,000 monthly, with COLA
Real return per month is (1%–0.5%)/1.005 = .4975%
I/YR = .4975*12 = 5.97%
P/YR = 12
N = 300
PMT = 3,000
FV = 0
Compute PV
Result: $466,942.12
10