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# Time Value of Money, Internal Rate of return

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Q1) Jill and Jack are making arrangement for their wedding in April 2012. The Romantic Garden Reception Centre says that they can pay \$5000 on 1Apr 2010, \$5000 on 1 April 20111 and \$10000 on 1April 2012. For the Bridal Bliss Wedding Centre the payments are \$2000 on 1 April 2010, \$5000 on 1 October 2010, \$6000 on 1 April 2011 and \$7000 on 1 April 2012.

a) If the money would otherwise be in a saving account which pays 4% per year interest compounded monthly (each calendar month), which would be the cheapest deal? Show all your working.

b) When you did the calculation in a), you made some assumptions (even if you didn't realize it). Write down at least three assumptions that you made.

Q2) You are given a business opportunity to invest \$12000 in Joe's Bakehouse. He offers to pay you \$6000 in two year's time and then \$11000 in 4 years' time.

a) Find the internal rate of return without using Excel.
(Hint, Sometimes a quartic equation can be viewed as a quadratic equation)

b) What does Theorem 1 for Existence and Uniqueness of IRR tell us for these cash flows? Explain your answer.

#### Solution Preview

Q1) Jill and Jack are making arrangement for their wedding in April 2012. The Romantic Garden Reception Centre says that they can pay \$5000 on 1Apr 2010, \$5000 on 1 April 20111 and \$10000 on 1 April 2012. For the Bridal Bliss Wedding Centre the payments are \$2000 on 1 April 2010, \$5000 on 1 October 2010, \$6000 on 1 April 2011 and \$7000 on 1 April 2012.

a) If the money would otherwise be in a saving account which pays 4% per year interest compounded monthly (each calendar month), which would be the cheapest deal? Show all your working.

To compare the deals we find the present value of the cash flows on April 1, 2010 by discounting the cash flows

Annual rate = 4%
Monthly rate = 0.3333% =4%/12

For annual cash flows (12 months) effective rate per year (period) = 4.07% =(1+0.3333%)^12-1

For half yearly cash flows (6 months) effective rate per half year (period) = 2.02% =(1+0.3333%)^6-1

Romantic garden Reception Centre:
Discount rate per ...

#### Solution Summary

The solution answers questions that determine the time value of money and internal rate of return.

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