#### 1008

##### Active Member
Hey everyone

Got a few finance questions from here and there for FINS1613...If anyone could help that would be awesome!

1) An investment makes annual payments. the first payment of $270 is due in one year at t =1. Payments grow at a rate of 16% annually until t=14. Payments then are stable until t=33. Afterwards, payments grow at a rate of 2% annually (the payment at t=34 is 2% bigger than the payment at t=33) and are paid in perpetuity. What is the present value of the investment's cash flows at an annual discount rate of 15%? 2) An investment makes annual payments. The first payment of$760 is due in one year at t=1. Payments grow at a rate of 11% annually until t=24. After this period, payments decline at a rate of 5% annually and are paid in perpetuity.You know that a 24 year annuity with a first payment of $1 growing at 11% annually is worth$14.3108. A similar 23 year annuity is worth $13.9257. What is the present value of the investment's cash flows at an annual discount rate of 15%? #### mreditor16 ##### Well-Known Member I would suggest posting them on the Academic Discussion Forum on Moodle! #### EinstenICEBERG ##### Einstein V2 I would suggest posting them on the Academic Discussion Forum on Moodle! except this is for a quiz #### mreditor16 ##### Well-Known Member Nws Pete! I know you're lurking #### Drongoski ##### Well-Known Member I'm going to read up on "Net Present Value" and come up with a solution. In fact I've just read a good 17 pages of a book I happen to have on Corporate Finance. (I found that I read this chapter in 2006!!) Last edited: #### Drongoski ##### Well-Known Member There are 3 income streams: A =$270 at t=1 growing at 16% annually for next 13 years (14 payments)

B = the last of the above payments for another 19 years (19 payments)

C = the constant payments in B, growing at 2% each year in perpetuity (I assume the 2% increase starts at t = 34)

Then:

$\bg_white A = \frac {270}{1.15} + \frac {270*1.16}{1.15^2} +\frac {270*1.16^2}{1.15^3} + \cdots + \frac {270*1.16^{13}}{1.15^{14}} \\ \\ = \frac {270}{1.15} \times\frac {(\frac {1.16}{1.15})^{14} - 1}{\frac {1.16}{1.15} - 1} \\ \\ B = 270 * 1.16^{13} \left [\frac {1}{1.15^{15}} + \frac {1}{1.15^{16}} + \cdots + \frac {1}{1.15^{33}} \right ] \\ \\ = \frac {270 \times 1.16^{13}}{1.15^{15}} \left[ 1 + \frac {1}{1.15} + \frac {1}{1.15^2} + \cdots + \frac {1}{1.15^{18}} \right ]\\ \\ = \frac {270 \times 1.16^{13}}{1.15^{15}} \times \frac {1 - (\frac {1}{1.15})^{19}}{1 - \frac {1}{1.15}} \\ \\ C = \frac {270 \times 1.16^{13}}{1.15^{33}} \left[\frac {1.02}{1.15} + (\frac {1.02}{1.15})^2 + (\frac {1.02}{1.15})^{3} + \cdots \right ] \\ \\ = \frac {1.02 \times 270 \times 1.16^{13}}{1.15^{33}} (\frac {1}{0.15 - 0.02})$

You then add up A, B and C

But if you are a typical 1st year Commerce or Finance student, are you expected to be able to handle this question ??

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#### Kaido

##### be.
^ Yes, this would be a standard growing annuity/perpetuity discounting to PV question

#### 1008

##### Active Member
Thanks everyone for you replies! I ended up getting the questions!

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