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Unformatted text preview: CARNEGIE MELLON UNIVERSITY Tepper School of Business INTRO FINANCE FIN 70-391 Prof. Spencer Martin Solution Set 2: Time Value Development Throughout this key, Annuity Factors and Discount Factors may be written: AF ( T, r %) = 1 r 1- 1 (1 + r ) T , and DF ( T, r %) = 1 (1 + r ) T . A MC 1. If the 4-year discount factor is 0.889 what is the 3-year rate of interest? No more than 4% if it were, what would we get?? 2. If the 2-year discount factor is 0.900 and the 3-year discount factor is 0.772, what is the present value of a 3-year annuity of $1 a year? Cant say theres no way to discount the first payment 3. Michael Parsnip has just taken out a $100,000 mortgage at an interest rate of 8%. If the mortgage calls for 20 equal annual installments, what is the amount of each installment? $10,185 4. See question number 3 What is the value of the mortgage (in second year dollars) after the payment of the second annual installment? $95,453 [subtract the PV of two payments, then advance that balance two years] 5. You own an office building. A fair rent for this building next year would be $100,000 and you expect that thereafter rents will increase indefinitely by 5% a year. Somebody has expressed an interest in renting the building at a fixed annual rent for 20 years. If the cost of capital is 15%, what would be a fair (i.e. equivalent) rental for 20 years? $160,000 [current value = 100 , 000 . 15- . 05 = $1 , 000 , 000 ] Solve: NewRent AF(20 yrs, 15%) = $1 , 000 , 000 $159 , 761 1 6. Suppose you have just won the lottery and must choose one of the following (guaranteed) payoffs....
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