ENGR 345 Engineering Economy Dr Lotfi K GAAFAR

ENGR 345 Engineering Economy Dr. Lotfi K. GAAFAR Eng. Ahmed Salah RIFKY 1

CASE STUDY Financing a House When a person or a couple decide to purchase a house, one of the most important considerations is the financing. There are many methods of financing the purchase of residential property, each having advantages which make it the method of choice under a given set of circumstances. The selection of one method from several for a given set of conditions is the topic of this case study. Three methods of financing are described in detail. Plan A and B are evaluated; you are asked to evaluate plan C and perform some additional analyses. The criterion used here is: Select the financing plan which has the largest amount of money remaining at the end of a 10 -year period. Therefore, calculate the future worth of each plan, and select the one with the largest future worth value. 2

Plan Description A 30 -year fixed rate of 10% per year interest, 5% down payment B 30 -year adjustable-rate mortgage (ARM), 9% first 3 years, 9. 5% in year 4, 10% in year 5 through 10 (assumed), 5% down payment C 15 -year fixed rate of 9. 5% per year interest, 5% down payment Other information: • Price of house is $150, 000. • House will be sold in 10 years for $170, 000 (net proceeds after selling expenses). • Taxes and insurance (T&I) are $300 per month. • Amount available: maximum of $40, 000 for down payment, $1600 per month, including T&I. • New loan expenses: origination fee of 1%, appraisal fee $300, survey fee $200, attorney’s fee $200, processing fee $350, escrow fees $150, other costs $300. • Any money not spent on the down payment or monthly payments will earn tax-free interest at 0. 25% per month. 3

Case Study Exercises: 1 - Evaluate plan C and select the best financing method. 2 - What is the total amount of interest paid in plan A through the 10 -year period? 3 - What is the total amount of interest paid in plan B through year 4? 4 - What is the maximum amount of money available for a down payment under plan A, if $40, 000 is the total amount available? 5 - By how much does the payment increase I plan A for each 1% increase in interest rate? 6 - If you wanted to “buy down” the interest rate from 10% to 9% in plan A, how much extra down payment would you have to make? 4

ANSWERS 1 - Evaluate plan C and select the best financing method. Price $150, 000 Down Payment $7, 500 Other Initial Costs $2, 925 Total Initial Costs $10, 425 Salvage Value $170, 000 Available Money/month $1, 600 Available Money $40, 000 Loan for $142, 500 Months 180 Interest/month 0. 79% Payments/Month $1, 488. 02 Actual Payment (T&I) $1, 788. 02 Money not spend at present $29, 575 The Actual Payment (T&I) exceeds the monthly available limit. Thus, Plan C is discarded. 5

2 - What is the total amount of interest paid in plan A through the 10 -year period? Plan A Interest = 0. 83% Loan Payments $142, 500. 00 $1, 250. 54 $385, 753. 41 $256, 166. 73 Balance at t=120 $129, 586. 68 Paid amount of loan $12, 913. 32 Interest Paid $243, 253. 41 FW at t=120 6

3 - What is the total amount of interest paid in plan B through year 4? Plan B Interest = 0. 79% Payment 1=payment of 0<t<4=at t=4 $51, 611. 15 Payment 2=payment of 4<t<5 at t=4 $14, 989. 56 Total Payments (1) $47, 184. 88 Total Payments at t=4 years $66, 600. 71 Balance at end of year 4 $138, 132. 42 Paid amount of loan $4, 367. 58 Interest Paid $62, 233. 13 7

4 - What is the maximum amount of money available for a down payment under plan A, if $40, 000 is the total amount available? Available Cash $40, 00 0 Origination Fee $1, 126. 26 Money Upfront: $40, 00 0 Money For DP using goal seek $37, 37 3. 7 4 8

5 - By how much does the payment increase I plan A for each 1% increase in interest rate? Interest Monthly Interest Payment 10% 0. 83% $1, 250. 54 11% 0. 92% $1, 357. 06 12% 1. 00% $1, 465. 77 13% 1. 08% $1, 576. 33 14% 1. 17% $1, 688. 44 15% 1. 25% $1, 801. 83 16% 1. 33% $1, 916. 28 17% 1. 42% $ 2, 031. 59 18% 1. 50% $2, 147. 60 19% 1. 58% $2, 264. 17 20% 1. 67% $2, 381. 20 9

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6 - If you wanted to “buy down” the interest rate from 10% to 9% in plan A, how much extra down payment would you have to make? Payment at i=10% $1, 250. 54 Payment at i=9% $1, 146. 59 Difference $103. 95 Interest=9%/12 0. 75% PV (difference ) $12, 919. 38 11