5-23 compute the present value, p, for the following cash flows. i = 10%

Explanation:

Step1: Recall present - value formula

The present - value formula for a single cash - flow $F$ received $n$ periods from now at an interest rate $i$ is $P=\frac{F}{(1 + i)^n}$.

Step2: Calculate present value of each cash - flow

For the cash - flow of $F_1 = 500$ at $n_1=4$: $P_1=\frac{500}{(1 + 0.1)^4}=\frac{500}{1.4641}\approx341.50$ For the cash - flow of $F_2 = 1200$ at $n_2 = 5$: $P_2=\frac{1200}{(1 + 0.1)^5}=\frac{1200}{1.61051}\approx745.06$ For the cash - flow of $F_3 = 500$ at $n_3=6$: $P_3=\frac{500}{(1 + 0.1)^6}=\frac{500}{1.771561}\approx282.23$ For the cash - flow of $F_4 = 1200$ at $n_4 = 7$: $P_4=\frac{1200}{(1 + 0.1)^7}=\frac{1200}{1.9487171}\approx615.80$ For the cash - flow of $F_5 = 500$ at $n_5=8$: $P_5=\frac{500}{(1 + 0.1)^8}=\frac{500}{2.14358881}\approx233.25$ For the cash - flow of $F_6 = 1200$ at $n_6 = 9$: $P_6=\frac{1200}{(1 + 0.1)^9}=\frac{1200}{2.357947691}\approx508.80$

Step3: Sum up the present values

$P=P_1 + P_2+P_3+P_4+P_5+P_6$ $P\approx341.50+745.06 + 282.23+615.80+233.25+508.80$ $P\approx2726.64$

Answer:

$2726.64$