Question

Question8Task 36 v4

Suppose the term structure of risk-free interest rates is as shown below:

Term (years)	1	2	3	4	5
Rate	1.99%	2.52%	2.74%	3.03%	3.63%

a. Calculate the present value of an investment that pays $1000 in two years and $2000 in five years for certain.

Answer: the present value is $. (round to two decimals)

b. Calculate the present value of an investment that pays $100 at the end of each of year from 1 to 5 for certain.

Answer: the present value is $. (round to two decimals)

c. If you wanted to value the investment in b. correctly using the annuity formula, which discount rate (%) should you use?

Answer: the discount rate is %. (round to three decimals)

(Hint: value correctly means that the present value of payments using the annuity formula equals the PV that has been computed in b.)

d. What is the shape of the yield curve given the term structure in the Table above?

Answer: Yield curve is . (fill in "increasing" or "decreasing")

Answer 1

(a). $ 1000 we get after 2 years, since the discount rate is different for each year, first we have bring $1000 from 2nd year to first year value. after that we have to again discount the 1st year value to the present value using 1st year discount rate.

Step 1 - Bring $1000 from 2nd year to first year value

First year value is $ 975.42

step 2 - Discount the 1st year value to the present value using 1st year discount rate.

So the present value of $1000 received after 2 years is $ 956.39

Similarly we have to calculate the PV of $ 2000 that will be received after 5 years

1. From 5 th year to 4th year

2. From 4th year to 3rd year

3. from 3rd year to 2 nd year

4. From 2nd year to 1st year

5.From 1st year to Present value

So the present value of $ 2000 received after 5 years = $ 1743.70

(b)

Total PV of cash flow = 464.32

(c)

here we have to use trial and error method, lets use r = 2.5% then the Present value comes to 464.58

Present value = 100*(1-(1+0.025)^-5)/0.025 = 464.58

So If you wanted to value the investment in (b) correctly using the annuity formula, the discount rate (%) should you use is 2.5 % (approx)