B Company's 16% required rate of return favors Alternative 2, offering monthly returns totaling $73,967.87, surpassing the staggered returns of Alternative 1 ($52,255.84).
Alternative 1:
Present Value at year 4:
PV4 = 50,000 / (1 + 0.16)^4
PV4 = 50,000 / 1.74058
PV4 ≈ 28,769.26
Present Value at year 7:
PV7 = 40,000 / (1 + 0.16)^7
PV7 = 40,000 / 2.57289
PV7 ≈ 15,527.69
Present Value at year 10:
PV10 = 30,000 / (1 + 0.16)^10
PV10 = 30,000 / 3.76947
PV10 ≈ 7,958.89
Alternative 2:
Monthly rate (16%/12):
r_monthly = 0.16 / 12
Number of months (10 years * 12 months):
n_months = 10 * 12
Present Value for Alternative 2:
PV2 = 750 * (1 - 1 / (1 + r_monthly)^n_months) / r_monthly
PV2 ≈ 73,967.87
Now, we compare the present values:
PV1 = PV4 + PV7 + PV10 ≈ 28,769.26 + 15,527.69 + 7,958.89 ≈ 52,255.84
B Company's required rate of return is 16%, and Alternative 2 yields a present value of $73,967.87, which is higher than Alternative 1 ($52,255.84). Therefore, B Company should choose Alternative 2.
The question probable may be:
The B Company has a policy of requiring a rate of return on investment of 16%. Two investment alternatives are available but the company may choose only one. Alternative 1 offers a return of $50 000 after 4 years, $40 000 after 7 years, and $30 000 after 10 years. Alternative 2 will return the company $750 at the end of each month for 10 years. What is the rate of return on investment that the B Company requires, and what are the details and returns associated with Alternative 1 and Alternative 2 in terms of time and amounts?