Mr Paul is identified three investment opportunities that he is considering.one is investment A that is expected to pay N$800.00 ayear for three years,followed by N$1000.00 per year for four years. it will pay N$2000.00 at the end of the eighth year.
Investment B is expected to pay N$3000.00at the end of the fourth year followed by N$400.00 indefinitely. Investment C will pay N$1000.00at the end of year 2,N$500.00 at the end of year 3,followed by N$400at the end of year 4,which will grow by 2%indefinitely.mr paul has required return of 10% on allhis investments.
Im struggle with this question
To determine the best investment option, we need to calculate the present value (PV) of each investment and compare them. The present value is the current worth of future cash flows, discounted by the required rate of return.
Let's calculate the present value of each investment option:
Investment A:
- Year 1 to 3: Cash flow of N$800 per year for 3 years
- Year 4 to 7: Cash flow of N$1000 per year for 4 years
- Year 8: Cash flow of N$2000
To calculate the present value of the cash flows, we need to discount them using the required rate of return of 10%. We'll use the present value formula:
PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow
r = Required rate of return
n = Number of years
Calculating the present value of each cash flow for Investment A:
Year 1: PV = 800 / (1 + 0.10)^1 = N$727.27
Year 2: PV = 800 / (1 + 0.10)^2 = N$661.16
Year 3: PV = 800 / (1 + 0.10)^3 = N$601.05
Year 4: PV = 1000 / (1 + 0.10)^4 = N$683.01
Year 5: PV = 1000 / (1 + 0.10)^5 = N$621.83
Year 6: PV = 1000 / (1 + 0.10)^6 = N$565.30
Year 7: PV = 1000 / (1 + 0.10)^7 = N$513.91
Year 8: PV = 2000 / (1 + 0.10)^8 = N$1118.69
The total present value of Investment A is the sum of all the present values:
PV(A) = N$727.27 + N$661.16 + N$601.05 + N$683.01 + N$621.83 + N$565.30 + N$513.91 + N$1118.69 = N$5482.22
Now, let's calculate the present value for Investment B:
Investment B:
- Year 4: Cash flow of N$3000
- From Year 5 onwards: Cash flow of N$400 indefinitely
Calculating the present value of each cash flow for Investment B:
Year 4: PV = 3000 / (1 + 0.10)^4 = N$2257.43
The present value of the cash flows from Year 5 onwards is calculated using the perpetuity formula, as the cash flow continues indefinitely:
PV = CF / r
Where:
PV = Present Value
CF = Cash Flow
r = Required rate of return
PV(Year 5 onwards) = 400 / 0.10 = N$4000
The total present value of Investment B is the sum of the Year 4 cash flow and the present value of the cash flows from Year 5 onwards:
PV(B) = N$2257.43 + N$4000 = N$6257.43
Lastly, let's calculate the present value for Investment C:
Investment C:
- Year 2: Cash flow of N$1000
- Year 3: Cash flow of N$500
- Year 4 onwards: Cash flow growing by 2% indefinitely
Calculating the present value of each cash flow for Investment C:
Year 2: PV = 1000 / (1 + 0.10)^2 = N$826.45
Year 3: PV = 500 / (1 + 0.10)^3 = N$378.79
The present value of the cash flow from Year 4 onwards is calculated using the growing perpetuity formula, as the cash flow grows indefinitely:
PV = CF / (r - g)
Where:
PV = Present Value
CF = Cash Flow
r = Required rate of return
g = Growth rate
PV(Year 4 onwards) = 400 / (0.10 - 0.02) = N$5000
The total present value of Investment C is the sum of the present values of each cash flow:
PV(C) = N$826.45 + N$378.79 + N$5000 = N$6205.24
Now, let's compare the present values:
PV(A) = N$5482.22
PV(B) = N$6257.43
PV(C) = N$6205.24
Based on the calculations, Investment B has the highest present value at N$6257.43. Therefore, Mr. Paul should choose Investment B as it offers the highest expected return based on his required rate of return of 10%.