1. K Company wishes to give its customers three options on payments for office e
ID: 391099 • Letter: 1
Question
1. K Company wishes to give its customers three options on payments for office equipment when the initial purchase price is over a certain amount. For example, the following three payment plans are options on a typical purchase, and K wants to be sure they are equivalent at a their TVOM of 14%. Determine the values of Q and R
End of Year
Option 1
Option 2
Option 3
0
$0
$0
$0
1
2,000
Q
R
2
2,000
2Q
(1.2)R
3
2,000
3Q
(1.2)2R
4
2,000
4Q
(1.2)3R
5
2,000
5Q
(1.2)4R
End of Year
Option 1
Option 2
Option 3
0
$0
$0
$0
1
2,000
Q
R
2
2,000
2Q
(1.2)R
3
2,000
3Q
(1.2)2R
4
2,000
4Q
(1.2)3R
5
2,000
5Q
(1.2)4R
Explanation / Answer
Present Value (PV) of Option 1 = $0 x 1.000 + $2000 x (1.14 + 1.300 +...+ 1.925) = 15071.037
For Option 2:
PV = $0 x 1.0 + Q x (1.14 + 2 x 1.300 + 3 x 1.482 + 4 x 1.689 + 5 x 1.925) = 15071.037
or, Q x (1.14 + 2 x 1.300 + 3 x 1.482 + 4 x 1.689 + 5 x 1.925) = 15071.037
or, Q x 24.567 = 15071.037
or, Q = 613.467
For Option 3:
PV = $0 x 1.0 + R x (1.14 + 1.21 x 1.300 + 1.22 x 1.482 + 1.23 x 1.689 + 1.24 x 1.925) = 15071.037
or, R x (1.14 + 1.21 x 1.300 + 1.22 x 1.482 + 1.23 x 1.689 + 1.24 x 1.925) = 15071.037
or, R x 11.744 = 15071.037
or, R = 1283.26
End of Year Option 1 Discount factors 0 $0 1.140 = 1.000 1 2,000 1.141 = 1.140 2 2,000 1.142 = 1.300 3 2,000 1.143 = 1.482 4 2,000 1.144 = 1.689 5 2,000 1.145 = 1.925Related Questions
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