Discounted Payback Question regular, required, discounted, question, investing

amqata

Hi all, just wondering how you calculate Discounted Payback quickly? Can it be done on the BA II (regular)? As you can fairly quickly get the payback period without much calculation can you go one step further to get the discounted payback?
Anyway the question is from Pg34 of the CFAI Book 4, Corporate Finance, Q6;
Kim Corporation investing 750m won, cash inflows of 175m won per year for 7 years. The required rate of return = 10%. Expressed in years, what is the (payback period &) discounted payback period?

franzino

BAII Plus Professional has it, not the BA II Plus. Here are the specs for both - I really don’t like the buttons on the professional one, you have to have strong fingers and press harder and pay attention to the inputs:
For BA II Plus:
http://education.ti.com/educationportal/sites/US/productDetail/us_baii_p...
For BA II Plus Professional:
http://education.ti.com/educationportal/sites/US/productDetail/us_baii_p...

ohai

CF outputs include discounted payback results in BA Plus Professional, not sure about other calculators.

mnieman

BA II professional can solve it quickly.
Here is how you would solve it using a regular BA II Plus:
First off, you’re going to use a little trial and error. Knowing that the NPV is the PV(Inflows) - PV(outflows), take the present value of the future income stream.
N = 7
I/Y = 10
PMT = 175
[CPT] [PV]
The answer you get is -851.97. Ignore the the sign and look at the magnitude: in this instance you have positive NPV.
So bump down the period by 1.
N = 6
[CPT] [PV]
Now you get -762.17. Again, ignore the sign. NPV will be positive, so you know that you’re discount payback period is less than 6 years.
Now try 5 years.
N = 5
[CPT] [PV]
The answer is -663.39. You need somewhere between 5 and 6 years to make up the total cost of the project. The NPV is -86.6123. Now we’re going to treat this as a single cash flow in year 6. So our next step is to inflate this value 6 years ahead.
Take that answer and plug it into PV
[2nd] [FV] (to clear TVM)
PV = -86.6123
I/Y = 10
N = 6
[CPT] [FV]
You get 153.439. This how much cash is needed in year 6. Since each year the cash flow is 175, you will 153.439/175 = 0.8768 additional years, in addition the 5.
Put these two figures together, and you get 5.8768. That is your discount payback.
The key is you’re trying to find the first year in which NPV becomes negative. That will tell you the minimum number of years you need to achieve your discount payback. Then, take the shortfall in NPV and inflate it to the following year. Once you find that future value, divide it by the CF for that year.
This is why I love the BAII Professional.