IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
A project requires an outlay of Rs 10,000 now and returns Rs 5,500 at the end of year 1 and Rs 6,050 at the end of year 2. What is the yield (internal rate of return) per annum effective?
The yield is 10.00% per annum. Discounting the two receipts at 10% gives Rs 5,000 each, which sums to the Rs 10,000 outlay, so the equation of value balances. Rates of 9% or 11% leave the present value of inflows above or below the outlay respectively.
- A8.50%
- B9.00%
- C10.00%Correct
- D11.00%
- 15.50%
Explanation
At i = 10%, PV of inflows = 5,500/1.1 + 6,050/1.21 = 5,000 + 5,000 = 10,000, which equals the outlay, so the equation of value is satisfied. At 9% the PV is about 10,138 and at 11% about 9,865, so neither balances. 15.50% is the total gain of Rs 1,550 as a percentage of the outlay, which ignores timing.
Did you get it right without looking?
One question tells you little. A timed set on Equation of value shows your real accuracy, how long you take and where you lose marks.
More Equation of value questions
- An investor puts Rs 10,000 into a deposit and receives a single payment of Rs 12,100 exactly two years later, with no other cashflows. What …
- An annuity-immediate pays Rs 1,000 at the end of each year for 5 years. Using an effective annual interest rate of 8%, what is its present v…
- A payment of Rs 1,00,000 is due in 4 years. The force of interest is 6% per annum constant. What is its present value, to the nearest rupee?
- A pension fund pays Rs 10,000 at the end of each year for 3 years. Using an effective annual interest rate of 10%, what is the present value…
- A loan of Rs 500,000 is repaid by five level annual instalments, the first due one year after the loan is made. The effective annual interes…
- A bank lends Rs 5,00,000 to be repaid by five equal annual instalments, the first paid one year after the loan is made. Interest is charged …