Terrified of “Returns” - Help me!

CFA Level I Quant
#1

Hello,

I am new to this forum. I have a fear of returns and calculating returns. This has always hindered me from pursuing finance, but I believe through practice I can become better. I have always avoided conversations in finance because of these problems. Maybe if I state my problems, somebody can help.

I don’t understand what it means when someone says “Oh this three year investment was great, it generated 3% return! I’'m glad I laid out my $100,000 into this project”

  • I don’t know how to calculate what the final amount he cashed out was

  • I don’t know how much money he had made in year 1 and year 2.

Can someone show me how I would know?

  1. I do not understand or know how to calculate when someone says, “make sure your return is greater than your cost of capital!”
  • I would be so grateful if someone can walk me through a basic example of how I can prove my return is greater than my cost of capital!

Sorry for the major rant, I’m just sick of not being able to get this down.

#2

FV = PV * (1+i)n

FV- future value after n years

PV - present value

i - interest rate

I - interest earned for year n = FVn - FVn-1

FV1 = 100,000 * 1.03 = 103,000; FV2 = 100,000 * 1.032 = 100,000 * 1.0609 = 106,090

FV3 = 100,000 * 1.033 = 100,000 * 1.092727 = 109,272.70

I1 = FV1 - FV0 = 103,000 - 100,000 =3,000

I2= FV2 - FV1 = 106,090 - 103,000 =3,090

I3= FV3 - FV2 = 109,272.70 - 106,090 =3,182.7

Grabe yerself a business math textbook: they tend to go into reasonable detail about compound interest math. If you want a very thorough, mathematical analysis of compound interest math, I suggest Theory of Interest by S. G. Kellison.

#3

Or in simpler terms: return is profit. If he invested 100,000 and made 3% return, that means he made 3000 on top of the original investment (so his portfolio value at the end of the year was 103,000). Nothing scary or complicated worth losing your sleep over. Obviously I’m simplifying here, there are many distinctions of return measures, before/after tax, nominal/real, etc., but no sense in going into them here.

Cost of capital…well, investments are by their nature risky (except if you invest in a risk free asset like us government bonds ). Investors require different level of return depending on how risky the respective investment is. If an investment is so risky that a reasonable investor requires 10% return per year for that level of risk, it would not make sense for you to invest in an asset with similar risk, which returns only 5%. Imagine if you have a firm, which is 99.99% financed by a bank loan with 10% interest per year. The cost of capital of the firm would be very close to 10%. If your profits are consistently less than 10% of your loan, you wouldn’t be able to repay even the interest of the loan after a while, let alone the principal.

In a similar fashion, equity investors also require return on their investment. And their case is even more dire, as in case of bankruptcy, employees, debt holders and suppliers will get paid first, and only of there’s anything left, it would be paid to them. So they carry a lot of the risk of the investment in the firm, so they require a commensurate returns for taking that risk.

#4

Thank you very much for the breakdown @breadmaker

Thank you Nenorr, however when you said " he invested 100,000 and made 3% return, that means he made 3000 on top of the original investment ", he actually ended up with 109,272; so 9,272 above his original investment. Again more confusion.

#5

Well, that’s he case if he kept all the money in that portfolio for 3 years, so roughly 3% per year ~ 9000 on top.

#6

Thank you very much (:

#7

Hey guys, you’ve helped me so much, I ran across one scenario today which I did not know how to find the “return” on:

CF0 = -100 CF1 = 40 CF2 = 30 CF3 = 80

I solved for IRR and I received 20%.

  • How can I set up the question so that I can prove I received 20% return (just like Breadmaker) did in his original response?

Thank you!

#8

Think of the investment as a bank account:

  • You deposit $100 today (CF0) at 20% interest per year.
  • One year from today you have $120 (= $100 + $100 × 20%). You take out $40 (CF1), leaving $80 in the account, still earning 20% per year.
  • Two years from today you have $96 (= $80 + $80 × 20%). You take out $30 (CF2), leaving $66 in the account, still earning 20% per year.
  • Three years from today you have $79.20 (= $66 + $66 × 20%). You take out $80 (CF3), closing out the account.

(The reason that it didn’t come out exactly zero at the end is that the IRR isn’t exactly 20%; it’s really 20.2607%, to 4 decimal places. If you redo the steps above with that rate, it will come out to zero, but the numbers will be messier.)

#9

Please tell me you let your calculator do the grunt iterations for the IRR problem. I would be very sad if you did it by hand with trial and error. :broken_heart:

#10

This is absolutely amazing, thank you!

So when we do IRR > Cost of capital, we use the same approach here?

If that $100 at Cf0 was taken through debt @10% interest, we use the same approach you did? Or do we just do 100(1+10%)4? In which case we get $141.6

If $141.6 is the total amount we must return, going back to my 20% IRR, I have:

  • $80 in year 1
  • $66 in year 2
  • $80 in year 3

correct?

#11

The cash flows in your example are fixed and remain so. The project needs an investment of 100 today in order to receive 40/30/80 at the end of years 1/2/3. Like S2000 stated, if this were a bank account, the equivalent rate of interest earned is roughly 20%/year. If my cost of capital is only 10%, it makes economic sense to invest the 100 in this project.

#12

So im indifferent between receiving those cash flows and between depositing $100 in a bank account for 20% interest.

I want to thank you both sincerely. This really has helped me.

Thank you magician and breadmaker, super appreciate it.

#13

My pleasure.

#14

Hello, I have stumbled again…

Can I please add a bit of context to this question so I can further expand my knowledge? I want to assume that the $100 I borrowed is from a bank that charges me 10% Interest (compounded interest), and assuming I do not pay any principle before the final year I created this table for clarity:

Year Cash Flow In Account You Take Out Net Account Interest Due Principle Due

0 -100 -100 N/A -100 0 0 1 40 120 40 80 10 0 2 30 96 30 66 11 0 3 80 80 80 0 12 133.1

Adding the you take out section we get 150 (and this is the total cash out amount we earned from this investment), and from this 150 we end up paying the 133.1 in debt, correct?

And hence the IRR > WACC equation holds true, HOWEVER, when I change the cost of capital to 15%, I get that I cannot make payment:

Year Cash Flow In Account You Take Out Net Account Interest Due Principle Due

0 -100 -100 N/A -100 0 0 1 40 120 40 80 15 0 2 30 96 30 66 17 0 3 80 80 80 0 20 152

I cash out at 150, but I owe 152 to the bank [100*(1+15%)3], therefore even if IRR > WACC, I still cannot pay, where am I going wrong with this?

Even at simple interest, if the cost of capital exceeds 16.7%, I cannot make payment. Now going back to what we said about being indifferent between a 20% bank account and the above investment, if there was a bank account offering 20% for my $100, then I would be inclined to think that I would earn $172.8 [100*(1+20%)3], therefore, I believe my cashing out amount is incorrect in my example?

#15

Your cash flows does not seem correct at all. First off, if you borrowed you need to have a cash inflow, not outflow in period 0. Next, your cash flows seem to make no sense. If you borrowed at 10% and you repay no principal until maturity, why is there a cash flow of 40/30/80 in periods 1/2/3? The interest should be 10 in each year, and in the last year you repay the principal of 100 as well.

My recommendation is not to make up examples and tables. Use actual problems if you want to learn the concepts. You cannot learn anything if your data is wrong to begin with - garbage in/garbage out concept.

#16

Hello Nennorr,

My Cash flows of 40/30/80 are from the fact that my IRR is 20% with my initial investment of $100. (as stated by S2000Magician):

  • You deposit $100 today (CF0) at 20% interest per year.
  • One year from today you have $120 (= $100 + $100 × 20%). You take out $40 (CF1), leaving $80 in the account, still earning 20% per year.
  • Two years from today you have $96 (= $80 + $80 × 20%). You take out $30 (CF2), leaving $66 in the account, still earning 20% per year.
  • Three years from today you have $79.20 (= $66 + $66 × 20%). You take out $80 (CF3), closing out the account

The 10% Interest is compounded, not simple interest and therefore the 10/11/12 to form 133.1 [100*(1+10%)3]

As for the inflow, maybe that is my mistake, I did not know that I have to factor in a (+) sign. But logically it is not adding up to make if this was a real-like investment.

*Note: Even if I add the $100, then my cash out is $250, which means I would still accept the project if the WACC > IRR (I tried it at 21% WACC)

#17

Here’s the breakdown as I understand it:

Loan:

  • You borrow 100 @ 10% interest (compound), which is equivalent to 11.03% simple interest for the period of 3 years - CF0 100

  • Periods 1 and 2 you pay interest of 11.03 - CF1 = -11.03 and CF2 = -11.03

  • Period 3 you pay the last interest and the principal - CF3 = -111.03

  • Net for the entire period you have cash outflow of 33.1 (the interest)

The investment:

  • You invest the 100 borrowed in an investment with IRR of 20%, so CF0 -100

  • In Periods 1/2/3 you cash out 40/30/80 from your investment.

  • Net for the entire period of the investment you have cash inflow of 50.

Since IRR > cost of debt (here, equivalent to WACC, since you financed the investment 100% with debt), we expect to make an overall profit.

Total net cash inflow from investment = 50, total net cash outflow from the loan = 33.1. Overall profit = 16.90.

Now, what seems to bother you in that scenario?

#18

Thank you for your input,

Using the same logic as above:

How come if we say IRR > WACC accept the project, if we take the same cash flows as above, but make interest at 15%, whereby IRR > WACC, we cannot make payment:

Investment: 50 net [150 total]

Loan: 52 net [152 total]

So IRR > WACC, but this is financially not feasible?

#19

Well, think about it. Keep in mind that IRR assumes that the returns are reinvested at the IRR rate. In general, the rule is applied when deciding whether to do a project or not. So you only decide by comparing the rates, without specifying the cash flows. BUT, if the cash flows are as you state, it would not make sense just to compare the IRR and WACC when you’re comparing with the financing as well. To be able to compare them, you need to be repaying part of the loans as you get these huge cash inflows from the project. Otherwise, you’re comparing apples to oranges - returns on a lower and lower principal (on the investment side), with interest on the full one (on the loan side).

Calculate what happens if you use the cash inflows to repay the loans, then you will note that the interest on the following periods will be lower.

#20

So we have just proven the fallacy of IRR > WACC?