Use the following rates for Questions 17-20.

Calculate ?3
Calculate ???1,2

Time

0y1y
1y1y
2y1y
3y1y
4y1y

Rate

3.00% 5.01% 7.03% 9.06% 11.10%

Consider an investment that will pay a cash flow of $1000 at t = 1. What is the value of this investment today (e.g., at t = 0)?
Now consider an investment that will pay a cash flow of $1000 at t = 4. What is the expected value of this investment in exactly 1 year (e.g., at t = 1).

Solutions

Expert Solution

17. Z3 means zero rates or spot rates for 3 years (like single rate for 3 years)

Z3 = ((1 + 0y1y) * (1 + 1y1y) * (1 + 2y1y))^(1/3) - 1

Z3 = ((1 + 0.03) * (1 + 0.0501) * (1 + 0.0703))^(1/3) - 1

Z3 = (1.157640)^(1/3) - 1

Z3 = 1.0500 - 1

Z3 = 5.00%

18. IFR(1,2) is the interest forward rate for 2 years 1 year from now

IFR1,2 = (1 + 0y1y) * (1 + 1y2y)^2 = (1 + Z3)^3

1.03 * (1 + 1y2y)^2 = 1.05^3

(1 + 1y2y)^2 = 1.157640 / 1.03

1 + 1y2y = 1.0602

1y2y = IFR1,2 = 6.02%

19. Value of $1000 at t=1 today = Cash flow / (1 + 0y1y) = 1000 / 1.03 = $970.87

20. Value of $1000 at t=4 after 1 year from today (t=1) = Cash Flow / ((1 + 3y1y) * (1 + 2y1y) * (1 + 1y1y))

Value of $1000 at t=4 after 1 year from today (t=1) = 1000 / (1.0906*1.0703*1.0501)

Value of $1000 at t=4 after 1 year from today (t=1) = $815.83

jeff jeffy answered 2 years ago

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