A $1,000 TIPS (Treasury Inflation-Protected Security) is currently selling for $
ID: 2806636 • Letter: A
Question
A $1,000 TIPS (Treasury Inflation-Protected Security) is currently selling for $967 and carries a coupon interest rate of 5.09 percent.
a. If you buy this bond, how much will you receive for your first interest payment, assuming no interest adjustment to principal during this time period?
b. If there's a 1.14 percent increase in inflation, what will be the new par value of the bond?
c. What is your new semiannual interest payment?
d. What would the par value be at maturity, assuming a 2.25 percent annual inflation rate and ten-year maturity period? Click on the table icon to view the FVIF table
.
Question a. - If you buy this bond, assuming no interest adjustment to principal during this time period, your first interest payment would be $_____ (Round to the nearest cent.)
Compound Sum of $1 (FVIF)
n
2.002.00%
2.252.25%
2.502.50%
2.752.75%
3.003.00%
11
1.0201.020
1.0231.023
1.0251.025
1.0281.028
1.0301.030
55
1.1041.104
1.1181.118
1.1311.131
1.1451.145
1.1591.159
1010
1.2191.219
1.2491.249
1.2801.280
1.3121.312
1.3441.344
1515
1.3461.346
1.3961.396
1.4481.448
1.5021.502
1.5581.558
2020
1.4861.486
1.5611.561
1.6391.639
1.7201.720
1.8061.806
2525
1.6411.641
1.7441.744
1.8541.854
1.9701.970
2.0942.094
Compound Sum of $1 (FVIF)
n
2.002.00%
2.252.25%
2.502.50%
2.752.75%
3.003.00%
11
1.0201.020
1.0231.023
1.0251.025
1.0281.028
1.0301.030
55
1.1041.104
1.1181.118
1.1311.131
1.1451.145
1.1591.159
1010
1.2191.219
1.2491.249
1.2801.280
1.3121.312
1.3441.344
1515
1.3461.346
1.3961.396
1.4481.448
1.5021.502
1.5581.558
2020
1.4861.486
1.5611.561
1.6391.639
1.7201.720
1.8061.806
2525
1.6411.641
1.7441.744
1.8541.854
1.9701.970
2.0942.094
Explanation / Answer
Bond Par Value =$1000, Market Value of Bond = $ 967 and coupon payments = 5.09 % per annum (assumed being paid semi -annually as part c is asking for the inflation adjusted semiannual coupon payments)
(a) The first interest payment is a coupon payment of (5.09 / 2 =) 2.545 % of bond face value, as coupon payments are semi annual in nature and also the first interest payment will come in at the end of the first 6 month.
Bond Face Value = $ 1000 and Semi Annual Coupon Rate = 2.545 % . Therefore, first interest payment (at the end of t=6 months) = Bond Face Value x Semi Annual Coupon Rate = 1000 x 0.02545 = $ 25.45
NOTE: This coupon value is calculated assuming no inlfation adjustment of interest rates.
(b) Increase in Inflation = 1.14 % . Current Bond Face Value = $1000
Therefore, Inflation Adjusted Bond Face Value = Inflation Rate x Current Bond Face Value - 1.0114 x 1000 = $1011.4
(c) New Bond Face Value = $ 1011. 4 . Coupon Payment Rate = 5.09% (semi - annual rate = 5.09 / 2 = 2.545 %)
Therefore, New Semi Annual Interest Payment = Semi Annual Coupon Rate x New Bond Face Value = .02545 x 1011.4 = $ 25.74
(d) If current par value is $1000 and the inflation rate is 2.25 % annually, then it implies that every year the bond par value would have to rise by 2.25 % to adjust for inflation. This inflation adjustment (or increment in par value) wll go on for 10 years (= bond maturity period).
Therefore, Inflation adjusted par value at maturity = Current Par Value x (1 + Annual Inflation) ^ (Bond Maturity)
= 1000 x (1.10225) ^ (10) = $ 1249.20
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