chapter 10 exam style question page 35

Hello. I need some help. Can you please tell me which in part v it says that the project is profitable at n=20? shouldn't it be n=10? according to page 37( we want the annuity > 32.852)

Can you please also explain me the way he calculates the profit? Shouldn't we calculate it according to page 17 of chapter 10?

That is A(20)(1+3%)^5 + annuity for 5 years?

Thanks in advance

 

Hi

I think this is just a confusion with your timeline. Project B has ten outgoings of -100,000 starting in year 0 and ending in year 9. This is followed by ten incoming payments of 45000V^10(IA)10 (45000, 90000, 135000 etc) that start in year 11 and end in year 20.

The value of the costs won't match the value of the income until somewhere in the latter period of the (IA)10 income. When we work it out we find that (IA)n reaches the required 32.852 when n = 9.632 years. Income payments are annual and so the dpp is when the 10th payment in the (IA) series is received, therefore in year 20.

As the DPP point is really 9.632 years, we have to accumulate the costs and income from 0 years up to 20 years at 7%. This gives 167,013. We now accumulate this at the profit rate of 3% up to 25 years as required in the question, giving the result of 193,600.

Hope this helps

Tim

 

it's clear now thanks a lot !

 

Shouldn't we get the same result though if we try to calculate the profit for the first project the same way as the 2nd's ?

I mean, cant we calculate the NPVa with i=7% and then accumulate this for 17,795 years with i=7% and then accumulate this result for 7,205 years at i=3%?

I get a different result (about 6,35)

 

The DPP occurs when the PV of the costs = the PV of the income. The income in project A is a continuous payment stream and we calculate the DPP to be at time 17.795 years. This means that when the payment is received at t=17.795, the PV of the income - PV of costs = 0. So there is zero to accumulate from t0 to t17.795. To get the accumulated value at t=25, all we need to do is calculate the income from the payment stream from t17.795 to t25.

Project B is different because no payment is received at the DPP point of t=19.632. So the project isn't "out of the red" until the payment at t20 is received. At t20, PV income - PV costs is not equal to zero. Therefore we accumulate (PV income - PV costs) at 7% from t0 to t20, and then accumulate that result at 3% from t20 to time 25.

I do think that the notes could be more detailed on this, and hope I've shed some light!

Tim

 

Thanks a lot Tim. so the difference in the calculation is because of the continuous payment if i understood correctly. I tried to calculate tha accumulated value to time 12.795 and it is zero as u mention..

 

Yes exactly - the fundamental difference between projects A & B is that A has continuous payment income and B doesn't. Or rather that in project A a payment is received at the time of the DPP whereas in project B no payment is received at the point in time where the DPP is calculated to be.

The exam Q is testing that you know how to find the accumulated value in either situation. I don't know yet but I'd guess that most exam questions on the DPP will involve this.

I'll be practising this a lot, as well as the damned compound increasing annuity calcs!

Tim

 

thanks a lot Tim for your help !

Yeah i also think the damned increasing annuities are sos though i havent started past papers yet !