The yearly cash flows of an investment are(-1000,-1200,800,900,800)
Is this a worthwhile investment for someone who can both borrow and save money at the yearly interest rate of 6%?
To determine the worthiness of the investment, we need to calculate the net present value (NPV) using the given cash flows and the yearly interest rate of 6%. The formula for calculating NPV is:
NPV = CF0 + CF1/((1+r)^1) + CF2/((1+r)^2) + CF3/((1+r)^3) + CF4/((1+r)^4)
Where:
- CF0, CF1, CF2, CF3, CF4 represent the cash flows at Year 0, Year 1, Year 2, Year 3, and Year 4 respectively.
- r represents the interest rate.
Substituting the given values:
CF0 = -1000
CF1 = -1200
CF2 = 800
CF3 = 900
CF4 = 800
r = 6% = 0.06
NPV = -1000 + (-1200/((1+0.06)^1)) + (800/((1+0.06)^2)) + (900/((1+0.06)^3)) + (800/((1+0.06)^4))
Now, let's calculate the NPV step-by-step:
Step 1:
NPV = -1000 + (-1200/((1+0.06)^1)) = -1000 + (-1200/1.06) = -1000 - 1132.08 = -2132.08
Step 2:
NPV = -2132.08 + (800/((1+0.06)^2)) = -2132.08 + (800/1.1236) = -2132.08 + 712.99 = -1419.09
Step 3:
NPV = -1419.09 + (900/((1+0.06)^3)) = -1419.09 + (900/1.191016) = -1419.09 + 754.75 = -664.34
Step 4:
NPV = -664.34 + (800/((1+0.06)^4)) = -664.34 + (800/1.26248) = -664.34 + 633.53 = -30.81
After calculating the NPV for all the cash flows, we find that the NPV is approximately -30.81. Since the NPV is negative, this indicates that the investment is not worthwhile at a 6% interest rate.
To determine whether this investment is worthwhile for someone who can both borrow and save money at a yearly interest rate of 6%, we need to calculate the present value of the cash flows and compare it to the initial investment.
The present value of a cash flow is the value of that cash flow in today's dollars, taking into account the time value of money and the interest rate. We can use the formula for present value:
PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow
r = Interest Rate
n = Number of Years
Let's calculate the present value of each cash flow:
PV1 = -1000 / (1 + 0.06)^1 = -1000 / 1.06^1 = -943.40
PV2 = -1200 / (1 + 0.06)^2 = -1200 / 1.06^2 = -1069.24
PV3 = 800 / (1 + 0.06)^3 = 800 / 1.06^3 = 677.97
PV4 = 900 / (1 + 0.06)^4 = 900 / 1.06^4 = 711.78
PV5 = 800 / (1 + 0.06)^5 = 800 / 1.06^5 = 711.78
Next, we sum up the present values of all the cash flows:
PV_total = PV1 + PV2 + PV3 + PV4 + PV5
= -943.40 + (-1069.24) + 677.97 + 711.78 + 711.78
= -911.11
The present value of the cash flows is -911.11. Since the initial investment is -1000, we can conclude that the present value of the cash flows is less than the initial investment.
Therefore, this investment may not be worthwhile for someone who can both borrow and save money at a yearly interest rate of 6%.