PS 1 Solutions

# PS 1 Solutions - Solutions to Problem Set 1 Corporate...

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Solutions to Problem Set 1 Corporate Finance, Sections 301 and 302 1. The present value formula is = \$280 1 + r If = \$250, then the discount factor, 1 / (1 + r ) must be: = 1 1 + r = \$250 \$280 = 0 . 8929 2. Similarly, if \$320 = \$400 1 + r , then r = \$400 \$320 - 1 = 0 . 25 so the discount rate is 25%. 3. The bond is a better investment. After 10 years, the PNC bank deposit will have grown to: = 550(1 . 045) 10 = 854 . 13 , which is lower than the face value (of \$1000) of the bond. 4. We first need to determine if the project is worth doing. Note that r = 15%, C 0 = - 5 , 000, C 1 = 6 , 000. Then = - 5 , 000 + 6 , 000 1 . 15 = 217 > 0 , so the project is worth doing. Lara starts with initial wealth of \$8000. The remaining part of her wealth = 8 , 000 - 5 , 000 = 3 , 000 should be invested in the bank at 15%. Hence the most Lara can consume in old age equals 6 , 000 + 3 , 000(1 . 15) = \$9 , 450 5. Again, the first step is to determine the NPV of the project. Using the same reasoning as in the above question, = - 12 , 000 + 15 , 000 1 . 18 = 712 > 0 . 1

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So James should undertake the project. Given that James will inherit \$3000 in his old age, the most he can consume now is \$712 + \$3000 1 . 18 = \$3254 . 37 . Note that to obtain this level of consumption, he borrowes the full amount, plus \$12,000 from the bank. In old age, he then pays this back with interest: (\$12 , 000 + \$3254 . 37)(1 . 18) = \$18 , 000 He can pay back \$18000 because of the \$15000 from the project, plus the \$3000 he inherits.
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