An investment on January 1 year 1 has expected receipts of on December 31 of each year of €900 for 4 years.The time value of money is 8%.What is the capital value as at January 1 for year 2.

Question

Quizplus · Accepted Answer

First, we need to calculate the present value (capital value) of the investment as at January 1 of year 1:
PV = (R / (1 + i)^n) + (R / (1 + i)^(n-1)) + ... + (R / (1 + i)^1)
PV = (900 / (1 + 0.08)^1) + (900 / (1 + 0.08)^2) + (900 / (1 + 0.08)^3) + (900 / (1 + 0.08)^4)
PV = 3025.47
Next, we need to calculate the present value of the expected receipts for the next 3 years (from January 1 year 2 to December 31 year 4):
PV' = (R / (1 + i)^n) + (R / (1 + i)^(n-1)) + ... + (R / (1 + i)^1)
PV' = (900 / (1 + 0.08)^2) + (900 / (1 + 0.08)^3) + (900 / (1 + 0.08)^4)
PV' = 2500.05
Finally, we can subtract the present value of the expected receipts for the next 3 years from the capital value as at January 1 year 1:
CV' = PV - PV'
CV' = 3025.47 - 2500.05
CV' = 525.42
However, since we want the capital value as at January 1 year 2, we need to calculate the future value of CV' for one year:
FV' = CV' x (1 + i)
FV' = 525.42 x (1 + 0.08)
FV' = 567.58
Finally, we can subtract FV' from the expected receipt for year 2:
CV'' = 900 - FV'
CV'' = 332.42
Again, since we want the capital value as at January 1 year 2, we need to calculate the present value of CV'' for one year:
CV''' = CV'' / (1 + i)
CV''' = 332.42 / (1 + 0.08)
CV''' = 307.76
Therefore, the capital value as at January 1 year 2 is €1376 (PV + CV''').

An Investment on January 1 Year 1 Has Expected Receipts