Answer:
Ans: $6,534
Explanation:
The given payment cash flows are described as follows:
1st payment in the year 0 = $222
Uniform annual payments of $222 are received at the end of years 1(is the same as the start of year 2) though 21
Uniform annual payments of $222 are received at the end of years 23 through 44.
The only missing payment in the uniform annual series is at the end of year 22.
a) PW of the given cash flow = $222 + $222(P/A, 2%, 44) - $222(P/F, 2%, 22)
b) (P/A, 2%, 44) = [(1+0.02)^44 - 1]/[0.02*(0.02+1)^44] = 29.080
(P/F, 2%, 22) = 1/(1+0.02)^22 = 1/1.02^22 = 0.6468
PW = $222 + $222*29.080 - $222*0.6468 = $6,534
Ans: $6,534
Answer:
Explanation:
Note : Rent received at the end of the year is equal to rent received at the beginning of a new year
1st payment received at the beginning of the 44 years period is termed payment received at year 0 = $222
so for the payments received at the end of year 1 in the second part of payment it is equivalent to rent received at the start of year 2 in the first part of payments and this through until the 21st year.
Identical payments are also received from year 23 to year 44 based on previous assumptions made BUT THERE IS NO IDENTICAL PAYMENT IN YEAR 22
A) applying equation for identical payments ( altered equation )
PW = $222 + $222(P/A, 2%, 44) - $222(P/F, 2%, 22)
PW of cash flow = identical cash flow per year + identical cash flow per year ( P/A, 2% , 44 ) - identical cash flow per year (P/F , 2% , 22 )
B) The net present value of the income system
(P/A ,2% ,44) = [tex]\frac{(1+0.02)^{44} - 1}{0.02*(0.02 + 1)^{44} }[/tex] = 29.080
( P/F , 2%,22 ) = [tex]\frac{1}{(1 +0.02)^{22} }[/tex] = 0.6468
back to the alerted equation
PW = $222 + $222* 29.080 - $222( 0.6468 )
= $6534
