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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 = 1.925