# Puzzling price of a bond

I was asked to solve this question: given a bond which grants the following cash flow (year $$t$$, return):

• (0, not reported)
• (1, 10)
• (2, 10)
• (3, 20)
• (4, 20)
• (5, 100)

What is the bond price in $$t=3$$ with flat rate of 3% per year for the entire financial operation?

Four possible choices:

• 90.71
• 113.68
• 120
• 130.23

I tried to solve with the formula of the Discounted Cash Flow but I obtained:

$$-x+\frac{10}{1.03}+\frac{10}{1.03^2}+\frac{20}{1.03^3}=0$$

i.e.

$$x=37.43$$

Can someone tell me where I am wrong? Thanks in advance.

• You have looked at the cash flows in years 1-3 discounted back to year 0. I suspect you may need to look at the cash flows in years 4-5 discounted back to year 3. Commented Jan 9, 2020 at 10:53
• I tried and both summing 4th and 5th term of DCF and summing 3rd, 4th and 5th, but the results are not contained in the choices above. Is it possibile that the four choices are wrong? Commented Jan 9, 2020 at 11:40
• With a 0% rate the value of the bond in zero is $160$, and with the same rate value of 0%, pushing in $t=3$ it is also $160$. So i would expect a value near $160$ in $t=3$ for that low rate. Something like $154.59$ would be the answer. Commented Jan 9, 2020 at 12:03

What is the bond price in $$t=3$$?
Try the cash flows in years $$4$$ and $$5$$ discounted back to year $$3$$, which in your terms means $$-x+\frac{20}{1.03}+\frac{100}{1.03^2}=0$$