What is the value of an investment that pays $44,000 every other year forever, i
ID: 2730784 • Letter: W
Question
What is the value of an investment that pays $44,000 every other year forever, if the first payment occurs one year from today and the discount rate is 18 percent compounded daily? (Use 365 days a year. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Value today $_________________
What is the value today if the first payment occurs four years from today? (Use 365 days a year. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value today $_____________________
Explanation / Answer
a) The value of an investment that pays $44,000 every other year forever, if the first payment occurs one year from today and the discount rate is 18 percent compounded daily:-
Effective two year interest rate (as the cash flows in this problem occur every two years):-
= [1 + 0.18 / 365]365 * 2 - 1
= (1.000493 )730 - 1
= 1.4330 - 1 = 0.433 or 43.3 %
Present value of perpetuity = 44000 / 0.433 = $ 101616.63 (approx)
(Note);- Assuming the payment made at the end of the compunding period.
Thus, value of investment today = 101616.63 / (1 + 0.18/365)365
= 101616.63 / (1.000493)365
= 101616.63 / 1.197
= $ 84892.76 (approx)
Conclusion:-The value of an investment that pays $44,000 every other year forever, if the first payment occurs one year from today and the discount rate is 18 percent compounded daily would be $ 84892.76.
b) The value today if the first payment occurs four years from today:-
Effective two year interest rate (as the cash flows in this problem occur every two years):-
= [1 + 0.18 / 365]365 * 2 - 1
= (1.000493 )730 - 1
= 1.4330 - 1 = 0.433 or 43.3 %
Present value of perpetuity = 44000 / 0.433 = $ 101616.63 (approx)
(Note);- Assuming the payment made at the end of the compunding period.
Thus, value of investment today = 101616.63 / (1 + 0.18/365)365* 4
= 101616.63 / (1.000493)1460
= 101616.63 / 2.0536
= $ 49482.19 (approx)
Conclusion:- The value today is $ 49482.19, if the first payment occurs four years from today.
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