Question

Treasury bonds with a face value of 1 million won, maturity of 3 years, interest rate of 5%, interest payment once a year, discount rate of 6%.

1. How many years is the Macaulay Duration of the above bonds?

2. How many years is the modified duet of the above bond?   

3. If the rate of interest is 10% (one-time annual payment), face value is 10,000 won, the present price of the bond is 9,600 won, and the price of the bond is 9,800 won after a year, what is the current yield rate, expected capital gain rate and expected return rate of the bond?

4. Can I buy a laptop with a present value of 1,020,000 won if I deposit 1,000,000 won in one-year bank deposits at a real interest rate of 2 percent and an expected inflation of 3 percent?

Same fluctuation as inflation rate)

Answer 1

1). Macaulay duration = 2.86 years

2). Modified duration = macaulay duration/(1+ annual yield) = 2.86/(1+6%) = 2.70 years

Note: Both these durations can also be calculated using the DURATION() & MDURATION() formulas in excel.

3). Annual interest payment = interest rate*par value = 10%*10,000 = 1,000

Current yield = annual interest payment/current price = 1,000/9,600 = 10.42%

Capital gains yield = (expected price/current price) -1 = (9,800/9,600) -1 = 2.08%

Expected return on the bond = current yield + capital gains yield = 10.42% + 2.08% = 12.50%

4). Nominal interest rate after 1 year = (1+ real rate)*(1+inflation rate) -1 = [(1+2%)*(1+3%)] -1 = 5.06%

If 1,000,000 is deposited now then after one year, we get 1,000,000*(1+ nominal rate) = 1,000,000*(1+5.06%) = 1,050,600

Price of laptop after 1 year = current price*(1+inflation rate) = 1,020,000*(1+3%) = 1,050,600

Both values are same, so yes, laptop can be bought after one year.