In this workout, we're being asked to calculate how much the return on equity is for this loan. And initially it might seem strange to have a return on equity for a loan because it seems like a weird mismatch of equity and debt. But it does make sense because although we are modeling a loan, what we're gonna do is we're gonna say because of bank capital ratios, there'll be a certain amount of equity that underpins that loan. And when banks are looking at their profitability, although it is interesting to them how much the loan is contributing and kind of what the return is on the loan, it's more interesting to figure out how much the return is on the underlying equity. Now the first thing to figure out is although the power value of the loan, so the face value of the loan is 100, and you can see that the interest rate on that face value will be 6. The amount that the borrower receives will not be 100. And that's because although there'll be 100 loan, that will be mitigated by the 2% fees.

And so you can see that the actual cash that we have to hand over is 98 as the bank. Because although you can imagine it as a hundred handed over, we immediately get 2 back in the form of fees.

The next thing we'll ask to do is to calculate the IRR. And although I'd love to use equals IRR just for simplicity, it won't work. And that's because equals IRR will only work when we have a string of cash flows. A bit like a project. Here what we have is we have repetitive cash flows, which are the interest. We have the initial outflow, which is the 98, and we have the maturity, which is 5. So we have the number of years where this relationship will persist. And so what we'll use instead is we'll use equals rates. Now you can see it's probably quite small for you, but just below the formula bar there, there's a good suggestion of how this thing works. Now it says N per, that's the number of periods. We've then got the payment and the payment will be on par. So although we kind of net only gave 98, we will receive 6 because the interest is paid on par. Now the PV is a bit tricky. It's the present value and it's the value today. So it is 98, that's the amount we're kind of handing over. We need to reflect that it's us handing that over. Because if we define the interest as a positive, this needs to be a negative. And so we need to turn that into a negative. Then finally, FV fair value, that's the redemption and that will happen at a hundred because they'll hand us back a hundred. Now for more complicated IRRs, the type and the guess would be important, such as IRR with two IRRs. But for us here, they're not important and we can skip them. And you can see the formula has popped up there and the internal rate of return is 6.5. And you can see that kind of makes sense because what's happening is we've got the return of the interest, that's 6%, but our overall return is higher than that and it's higher due to the fees. And so the fees are creating additional return. And that's being reflected in the IRR there of 6.5.

Let's start moving down and going to a bit more real world stuff. What would happen in the bank and how that would translate to returns? So the interesting income, what's gonna happen is we have lent out 98 and we're effectively gonna reverse what we just did and we will be earning on a yearly basis, 6.5. And you might be wondering why we're not using the 6 there. What we're doing here is we're wrapping up the fee into the income.

So next, the interest expense, and this is the expense of the bank, remember. So we're making a certain amount of income from the the borrowing, and now we have to pay our depositors as the bank. And so what we've got to do is we've got to say, well, we just handed over 98 and a certain amount of that, and not all of it, but a certain amount of it, about 85% of that will be represented by deposits. And those deposits will have a cost. And that cost is the bank's cost of financing. So we have to reward our depositors with 3%, and that means our interest expense is 2.5 and the net interest income will be a netting out of those two. And so you can see that the bank is making 3.9. Next we have rewarded our depositors and that's good, but we also have all the staff of the bank to reward. And so according to the assumptions we've got here, you can see the expenses are a percentage of the net interest income. And so if we make 3.9 of income, half of that goes to expenses straight away. And so if we net those two out, we've got profit before tax of 1.9. Next we're gonna have to pay tax on that. So let's go and find the tax rate and that's 20%.

And so we end up with net income of 1.5 once all our costs have been satisfied. Now before we apportion the 98 into the deposits, and we're now gonna do the other part of that, which is the equity. So if we say, okay, well we just handed 98 over and so we made a loan of 98, 15% of that according to the rules have to be backed by equity. And so we've got equity of 14.7, and now what we can do is we can put the net income relative to that equity and this gives us the return on equity of 10.5%.