Question

Investment X offers to pay you $4,200 per year for eight years, whereas Investment Y offers to pay you $6,100 per year for five years.
a. Calculate the present value for Investment X and Y if the discount rate is 5 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)b. Calculate the present value for Investment X and Y if the discount rate is 15 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

PVxa = $27,132.00, PVya = $26,413.00,

Explanation:

Present value (PV) is the value of the future expected cash flow. PV rests on the idea that the worth of a cash received is more than that of the cash promised to be received in the future. To calculate PV a stream of incomes to be received a number of period in the future, the following formula is used:

$PV = C[\frac{1-(1+r)^{-n} }{r} ]$

Where PV = present value

C = cash flow amount from the investment

r = discount rate

n = number of period, in this case years, to receive the cash flow.

The PV formula above is therefore employed to answer the question as follows:

Answer to question (a)

For Investment X in question (a)

PVxa = $4,200 * {[1-(1+r)^-n]/r}

PVxa = $4,200 * {[1-(1+0.05)^-8]/0.05}

PVxa = $4,200 * 6.463212759

PVxa = $27,145.49      

For Investment Y in question (a)

PVya = $6,100*{[1-(1+r)^-n]/r}

PVya = $6,100*{[1-(1+0.05)^-5]/0.05}

PVya = $6,100 * 4.329476671

PVya = $26,409.81  

Answer to question (b)

For Investment X in question (b)

PVxb = $4,200 * {[1-(1+r)^-n]/r}

PVxb = $4,200 * {[1-(1+0.15)^-8]/0.15}

PVxb = $4,200 * 4.487321508

PVxb = $18,846.75  

For Investment Y in question (b)

PVyb = $6,100*{[1-(1+r)^-n]/r}

PVyb = $6,100*{[1-(1+0.15)^-5]/0.15}

PVyb = $6,100 * 3.352155098

PVyb = $20,448.15  

Where PVxa, PVya, PVxb and PVyb represents PV for X and Y in questions (a) and (b).

Decisions:

1. In question (a) part where the PV of $27,145.49 of X is greater than $26,409.81 of investment Y, it is better to invest on investment X.

2. In question (b) part where the PV of $20,448.15 of Y is now greater than $18,846.75 of investment X, it is better to invest on investment Y.