FIN 48 Calculating Bid Price

Let's examine problem 778. Computing a bid price. This is a difficult problem. I find the algebra here to be a little bit tricky, a little bit confusing, but if you get lots of reps in, and my workbook certainly has lots of practice, you can get there. Let's go through it. Digico Gaming has put out a request for proposal asking for a company to supply it with 500,000 USB ports annually over the next four years. The USB ports are for use in their handheld gaming system. Your company makes USB ports and the CFO has asked you to prepare a bid on the RFP. Winning this bid will require significant capital investments for your company as there are some custom elements to the RFP. Your company will need to invest $2.1 million in fixed assets and you'll need to increase working capital by $300,000. The fixed asset investment will be depreciated over the four-year life of the project down to zero. So if we have a $2.1 million investment that we're depreciating down to zero over four years, that computes to, I think I can do this in my head, heaven help me, I hope I'm right, $525,000 per year in depreciation. Okay so I don't know if I'm going to use the number yet but that is my depreciation, my annual depreciation cost. The assets will have salvage value of $250,000. Okay so another little calculation we can do here if we have a tax rate which we do is to say what is my net salvage value. So if I depreciate the thing down to zero, I sell it now for $250,000. There's tax implications. I have a $250,000 recapture for tax purposes which will be taxed at a 20% tax rate so that's $50,000 in tax meaning when I sell a $250,000 item and I pay $50,000 in taxes, my cash flow from salvaging this is going to be $200,000. Okay so again holding that number off to the side, that's just a number floating in the back of my mind at this moment. Your fixed production cost for the project will be $400,000 a year and variable costs will be $1 per unit and we're doing 500,000 units annually for four years so you know it's $500,000 in variable costs a year so our fixed costs were $400,000. Our variable costs were not $900,000, $500,000 and it's just 500,000 units times $1 per unit so $400,000 plus $500,000 is $900,000 and that is our total costs. Okay your company's required rate of return on the project is 10% and as we said the tax rate is 20%. So how to solve this thing? It's a lot of information but it hasn't given us key information because we have to solve for it. It hasn't given us the price right? What's our sales price? What's our sales going to be on this project? And the answer is if we want to price the bid aggressively we have to price it to have a rate of return of 10% on the project. So let's go through our cash flows and kind of see what that looks like. So here's what we know. In year zero our cash flows are going to be the cost of investing in the new assets and also the cost of tying up more working capital. So 2.1 million negative cash flow and a $300,000 negative cash flow. In year one we're going to have operating cash flows of question mark. It's going to depend on how much we price the product at. So I'm going to call this x right? We're solving for this. This is the variable we need to solve for to figure out our price. In year two again we don't know what our operating cash flows are going to be. Year three we don't know what our operating cash flows are going to be. Year four we don't know what our operating cash flows are going to be. But at the end of four years we do have some cash flows that we do know what they're going to be. This is an x. It's the ugliest x in my life. You know you have uniquely messy handwriting when you can't write an x. Very neat. It's a challenge of my life. I write on computer screens for a living and my handwriting is messy. It's I don't know a terrible irony or curse or something. Let's continue. So what cash flows do we know in year four? We know that um let's see we need to we needed to increase our working capital by 300 but we get that back at the end of the project. We no longer have this special project so we no longer have this working capital set aside. We might take on new projects but we'll deal with those at that time. And the other thing is we're going to salvage the asset and we said salvaging the asset is going to give us two hundred thousand dollars in positive cash flows. Okay so what our first step towards solving this is solving for x which is our OCF our operating cash flow. So let's try to figure out what our operating cash flow needs to be in order to meet our 10 percent required rate of return. How do I do that? Well the first step is it's kind of a weird one. We'd like to figure out what these lump sums are. In other words we just want to clear them off the table here. And how do I clear them off the table? I put them into year zero dollars and then this just becomes an annuity right. It's an annuity where we don't know the annual payment amount but it's the same payment every year. So clear these off the table by discounting the cash flows. That's what we do here. We discount cash flows. Let's discount the cash flows that we're able to discount. So this is five hundred thousand dollars in cash flow in year four. So we go five hundred thousand divide by one plus the discount rate which is ten percent. 1.1 to the power of four and whatever number we get there we will write at the top. So 1.1 to the power of four is 1.461. Look at this. I did something funky with my graphics here. Interesting. Anyway 4.461. I go one over x and I multiply by five hundred thousand three four one five oh seven. Okay so this is a positive cash flow three four one five oh seven in today's dollars. So again we're trying to get set net present value to zero. This is sort of the minimum the most aggressive bid price. That's what we're going for here. And we could certainly bid higher than the most aggressive bid price but we would never want to bid lower. It would result in a negative net present value. But an appropriate bid price is the most aggressive. We'd like to win the bid. So negative 2.1 million minus three hundred thousand plus three four one five oh seven. Let's figure out what that adds to. 2.1 million negative minus three hundred thousand plus three four one five oh seven gives us two oh five eight four nine three two oh five eight four nine three. Don't forget the negative. And okay so that's the present value of our year zero stuff as well as the year four stuff that we knew had a present value. And what we need to say is we want net present value to be zero. So the sum of these four cash flows need to add to two oh five eight four nine three. This is an annuity. We know the present value of the annuity is two oh five eight four nine three. We know the number of periods certainly is four. We know the required rate of return is 10 percent. We know the future value is going to be zero so we can compute the recurring annual payment the operating cash flow in this case. Now I can do this by hand and in fact I will at the end of the video just show you how to do this one by hand but I do prefer using a financial calculator. Your professor may differ from me but I would allow my students to use a financial calculator to do this. But if yours doesn't it's fine you can definitely do this by hand. It's a few different ways but we'll just do it with formulas. So two oh five eight four nine three is our PV. N is four. Ten is our required rate of return. And zero is our FV. And now I'm going to compute my PMT. I get six four nine three nine four. Six four nine three nine four. Okay so that is the annual operating cash flow. Six four nine three nine four. But this still isn't my bid price right? This is just my annual operating cash flow. So how do I go from operating cash flow to a bid price? Well we've got a few different ways to derive operating cash flow and the one we're going to want to use here is the tax shield method or the tax shield approach to calculating OCF. Here's the formula for the tax shield approach and the reason is we we have all the information we need if we use the tax shield approach otherwise it's tougher or impossible. So here's the formula for the tax shield approach for operating cash flow. Remember what the tax shield approach says. It says okay take your sales minus all your costs. Pretend there's no such thing as depreciation and just figure out the cash flows. Sales minus costs. You net out the taxes and then you say okay that's basically my cash flow. And then at the end the last step is you say well depreciation didn't involve cash but how much tax did depreciation save us from? And so in a separate step you figure out the depreciation tax shield and add it back in. So that's what we're going to do here because we have all the information. So sales minus costs times one minus the tax rate. That'll give us sales minus costs net of tax plus the depreciation hopefully I'm not yeah I'm good depreciation tax shield. How much money does depreciation how much cash does depreciation save us? So let's start with sales minus cost. So we know our operating cash flow. Sorry I'll start there. We know our operating cash flow is six four nine three nine four. We don't know our sales minus cost. I'm going to treat this as a single variable sales minus cost. We know one minus the tax rate. Tax rate is 20 percent. So one minus the tax rate is 0.8. So sales minus cost times 0.8 plus the depreciation tax shield. Well what's that? Our depreciation we said was five hundred and twenty five thousand dollars per year. So what's the tax shield? Well it saves us 20 percent on taxes right reduces our tax load by 20 percent. So how much did depreciation reduce your tax burden? 525 times 0.2 hundred and five thousand dollars. That's our depreciation tax shield 105 000. So now let's solve for everything except for our variable sales minus costs. Okay so let's subtract 105 from both sides. So six four nine three nine four minus 105 000 five four four three nine four equals sales minus costs times 0.8. Divide both sides by 0.8. So divide by 0.8 and it's 680 490. I'm going to call it 493 680 493 equals sales minus costs. And in fact we know our costs. Our costs are nine hundred thousand dollars. So 680 493 equals sales minus 900 000. So let's add back the 900 000 to both sides. So we get sales equals 1580 493. Okay so for us to have a net present value of zero we need to make a bid that produces sales of one point almost 1.6 million. Right we need to make a bid that produces 1.6 million dollars in sales. We are selling or bidding on 500 000 usb ports annually and I need to make a bid that produces revenues of 1.5 million. What do I do? I just divide this by 500 000 the number of usb ports and that's going to give me a sales price of divide by 500 000 3.161 per port. That's our bid. So that's the most aggressive bid we do ever want to give. Certainly there might be strict strategy or whatever but if you want to sort of place a competitive bid your best bid is 3.161. You're not going to go below that. So there we go. That would be an appropriate bid price. That's how we compute it. We have solved problem 77a. I promised I'd do some stuff by hand. I'll do it after. I give a little self-promotion if you made it to the end. I hope you like and subscribe. As promised I said I was going to compute this PMT by hand. To do it we need the present value of an annuity formula. So PV of an annuity equals the amount of the payment times 1 minus 1 over 1 plus i to the power of n all divided by i. Okay and now we're just solving for PMT. Right so we know the PV of our annuity negative 2058493 or just I think we just leave it as a positive 2058493. We don't know our PMT. Let's figure out what's in this square bracket. 1 minus 1 over 1.1 to the fourth power for year period all divided by 0.1. So let's get that whatever's in the brackets there that multiplier 1.1 to the power of 4. 1 over x 0.68 1 minus that so I go minus 1 I hit the plus minus button I'm at 0.3 I divide by 0.1 and the thing in the brackets is 3.1698 and so on 3.1699. Okay so now I divide both sides by 3.1699 and I'll have solved for my payment. So I just go 1 over x times 2058493 2058493 and I get 649394 as my payment. PMT equals 649394 and then you know we're off to the races. So the bottom line here was I just wanted to show you did not need a financial calculator if you're in a class that doesn't have one. This is still very much a solvable problem. It didn't take me long right took me an extra 30 seconds maybe. All right we've done it and for goodness sakes I hope you liked it and if you did I hope you give me a thumbs up. Have a great day. Bye.