Coronado Inc. has $520,640 to invest. The company is trying to decide between two alternative uses of the funds. One alternative provides $69,086 at the end of each year for 12 years, and the other is to receive a single lump-sum payment of $1,633,990 at the end of the 12 years. Which alternative should Coronado select

None of the alternative should be selected by Coronado Inc.

Explanation:

This can be determined by comparing the net present value of the 2 alternative.

The fisrt thing to do is to calculate the simple interest to be used as follows:

Simple rate of return = Annual return / Investment cost = $69,086 / $520,640 = 0.1327, or 13.27%

Step 1: Calculation of the net present value of alternative that provides $69,086 at the end of each year for 12 years

We have to first calculate the present value using the formula for calculating the present of an ordinary annuity as follows:

PV$69,086 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV$69,086 = Present value of the annual cash flow of $69,086 = ?

P = Annual cash inflow = $69,086

r = Simple rate of return = 0.1327, or 13.27%

n = Number of years = 12

Substitute the values into equation (1) to have:

PV$69,086 = $69,086 * ((1 - (1 / (1 + 0.1327))^12) / 0.1327) = $403,899.27

The net present value can now be calculated as follows:

NPV$69,086 = PV$69,086 - Investment cost (2)

Where;

NPV$69,086 = Net present value of alternative that provides $69,086 at the end of each year for 12 years = ?

PV$69,086 = Present value of the annual cash flow of $69,086 = $440,303.13

Substitute the values into equation (2) to have:

NPV$69,086 = $ 403,899.27 - $520,640

NPV$69,086 = -116,740.73

Step 2: Calculation of the net present value of alternative that  pays a single lump-sum payment of $1,633,990 at the end of the 12 years

We have to first calculate the present value using the present value formula as follows:

PV$1,633,990 = $1,633,990 / (1 + r)^n (3)

Where;

PV$1,633,990 = present value of $1,633,990 = ?

r = Simple rate of return = 0.1327, or 13.27%

n = Number of years = 12

Substitute the values into equation (3) to have:

PV$1,633,990 = $1,633,990 / (1 + 0.1327)^12 = $366,328.40

The net present value can now be calculated as follows:

NPV$1,633,990 = PV$1,633,990 - Investment cost (4)

Where;

NPV$1,633,990 = net present value of alternative that  pays a single lump-sum payment of $1,633,990 at the end of the 12 years = ?

Substitute the values into equation (4) to have:

NPV$1,633,990 = PV$1,633,990 - Investment cost = $366,328.40 - $520,640 = -$154,311.60

Conclusion

Since the NPVs of the two alternative are negative, none of the alternative should be selected by Coronado Inc.