# Discounted Payback Question

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?

Using the regular BA II Calculator - you have to go the hard route for Discounted Payback. With the BA II PLus == you have an option which gives you the DPB directly. CP

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_plus.html?bid=5 For BA II Plus Professional: http://education.ti.com/educationportal/sites/US/productDetail/us_baii_plus_pro.html?bid=5

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

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.

gdiddy There is an even faster way with the BA II Plus professional. 2nd CF CF0 = -750 down arrow C01 = 175 down arrow F01 = 7 down arrow This is setting up the project. Hit NPV button It asks for I enter 10 hit Enter down arrow --> 101.973 hit down arrow NFV hit down arrow PB hit compute --> 4.2857 hit down arrow DPB hit compute --> 5.876 You have your answers directl and you do not need to find / interpolate between values as you have done. This feature is present only on the BA II Plus professional. Thought I would share it with you. CP

Oh I know that. But that feature is not available on the regular BA II Plus. I was showing how people with the BA II Plus can do the calculation. That’s why I mentioned at the end of my post why I love owning the BA II Professional. I still have my BA II Plus for almost 8 years, and every now and then I’m use it during my studies.

ok, thanks!! looks like i should have bought the professional model…! fingers crossed(for people who have the regular model) it doesn’t come up!

A tip for HP12c users…

I haven´t found a way for DPP, but the possible answers (a,b,c) can make it easier.

For the Kim Corporation example we can see that the DPP will be at least 5 years. We can quickly calculate the NPV after 5 years and see that it is -86mil. Find the PV of the next cash flow and divide that into 86 for the interpolation.

DPP = 5 + 86/98

Sounds complicated, but it can be done pretty quickly.

Mark

I take it HP doesn’t have a way of doing this quickly?

When I bought my calculator (regular BA II Plus) I knew that it didn’t have this option, yet I still bought the regular one. Why? Because the buttons of the Plus Professional are hard to press and you must pay attention to your button presses to make sure they’ve been registered. The buttons on the Plus outweigh the discounted payback function for me.