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Homework answers / question archive / Bonds You are considering purchasing the following bond: Face Value: 1,000,000 SEK Coupon rate: 5
Bonds You are considering purchasing the following bond: Face Value: 1,000,000 SEK Coupon rate: 5.0 % (coupons are paid once per year) Time to maturity": 30 years The yield to maturity of the bond is 6 %. a) What is the price of the bond today? b) For the same bond in item a, assume that we wish to sell it in 10 years' time after the coupon has just been paid and that the yield to maturity has dropped to 5 % by then. What price do we receive when we sell the bond?? c) Use the table in the answer sheet and indicate the cash flows received from an investment consisting in buying the bond 30 years before its maturity, keeping it for 10 years and selling it right after coupon number 10 is paid (the investment in year o, the coupon payments and the payment received when we sold the bond at the price computed in item b). Use the values actually paid out those years, not the present value. Also, indicate by using the sign + or - if it was a cash outflow or a cash inflow). Also called the "term" of the bond A tip here, the bond had 30 years until it matured when we purchased it. Now we have been holding onto it for 10 years, what is now the time to maturity of the bond?
Given Information
Face Value (FV) = 1,000,000 SEK
Coupon Rate =5% per annum
Coupon Amount (c) = 5% * 1000000 = 50,000 SEK
Time to maturity = 30 years
Yield to Maturity (r) = 6%
a)
Bond Price (Present Value) Calculation
Price of Bond (P) = c/ (1+r) + c/ (1+r)2 +………….+ c / (1+r)N + FV / (1+r)N
=> P = {c * [(1+r)N – 1]} / [r * (1+r)N ] + FV / (1+r)N
where
P – Bond Price = ?
c – Coupon Amount = 50,000 per annum
N – No of periods = 30 years
FV – Face value payment at maturity = 1,000,000
r – interest rate (YTM) = 6% per annum
So, Price of bond today = {50000 * [(1+0.06)30 – 1]} / [0.06 * (1+0.06)30 ] + 1000000 / (1+0.06)30
= 862,352 SEK
b) After 10 years, remaining maturity (N) = 30-10=20 years
Yield to Maturity (r) = 5%
So, price of bond after 10 years = {c * [(1+r)N – 1]} / [r * (1+r)N ] + FV / (1+r)N
= {50000 * [(1+0.05)20 – 1]} / [0.05 * (1+0.05)20 ] + 1000000 / (1+0.05)20 = 1,000,000 SEK
c) Year wise cash flow are as follows
|
Year |
Cash Flow |
|
0 |
-1,000,000 |
|
1 |
+50,000 |
|
2 |
+50,000 |
|
3 |
+50,000 |
|
4 |
+50,000 |
|
5 |
+50,000 |
|
6 |
+50,000 |
|
7 |
+50,000 |
|
8 |
+50,000 |
|
9 |
+50,000 |
|
10 |
+1,050,000 (=50000+1000000) |
