In: Finance
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).
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