Answer: at $194.6673, it is a good deal to invest
Explanation:
From the statement made by the bank that investors should pay $100 per year for 10 years to get a return of $100 per year forever at an interest rate of 6%, we would need to calculate the Present net value to determine if this is a good deal.
Present net value = Present value of Perpetuity - Present value of Annuity
let us solve for each;
⇒ Present value of annuity in year 0
Present value = payment made × [(1- 1/(1+interest rate)yrs) / interest rate]
= $100 × [(1- 1/(1+6%)¹⁰) / 6%]
= $100 × [(1- 1/(1.06)¹⁰) / 0.06] = $100 ˣ 7.360087
Present value of annuity₀ = $736.0087
⇒ Value of Perpetuity in year 10
Present value of Perpetuity₁₀ = Amount / Rate
= $100/6% = $100/0.06 = $1666.7
∴ Present value of Perpetuity₁₀ = $1666.7
⇒ Present value of perpetuity in year 0
Present value of Perpetuity₀ = Value of Perpetuity in the end of year 10 / (1 + Rate)ⁿ
where n = no of years
= $1666.7 /(1 + 6%)¹⁰ = $930.676
Present value of Perpetuity₀ = $930.676
Therefore the Net Present value = Present value of perpetuity(inflow) - Present value of annuity(outflow)
Therefore the Net Present value = $930.676 - $736.0087 = $194.6673
⇒This means that the net present value of the investment is a positive value i.e. $194.6673, so it is a good deal of investment.
cheers i hope this helps.
