 Hello in this lecture. We're going to work some test type problems problems that are short enough to fit in multiple choice type questions First we have a company must repay the bank a single payment of 21,000 cash in two years for a loan it entered into the loan is at 10% Entries compounded annually the present value factor for two years after 10% is 0.8264 the present value of the loan is what so we have we have the loan that we're going to pay back What would be the present value basically after two years? Considering a 10% interest rate now the easiest way to do this would basically be to look at a table in order to find the Rate here the present value factor which they gave us so we don't need the table right now So they made it pretty straightforward in the multiple choice question We're just going to take that 21,000 and since it's two years time And if we looked up in the table and they said that it was a two years at 10% And they gave us the factor of 0.8264 then I'm going to go ahead and add decimals go to the home tab numbers add Four decimals gonna underline home tab font underline then we're just going to say this equals the 21,000 Times the factor that was given to us and so therefore the present value today's value of the seven is 17354 if we were to pay back the loan of 21,000 after two years at 10% Next one says a company borrowed cash from the bank by signing a seven year eight percent installment note The present value of an annuity factor at eight percent four seven years is five point seven oh six four Each annual payment is 42,255 and 69 cents the present value of the note is what so we have kind of the opposite here now Now we have basically an annuity as long as the annuity is constant Then once again the easiest way to do that is to look at the annuity table and figure out what the value would be and they gave us That factor again assuming the eight percent seven years. We're gonna have the five point two oh six five So now we have constant payments of forty two two five five point six nine I'm gonna go. I'm gonna highlight all of these and go to the home tab Numbers add the pennies on to that and then we're just gonna multiply that times the five point two oh six four That's the amount we would find in On the annuity table based on seven years if we found that the table would have seven years and then eight percent That would be at that section. We're gonna go to the home tab. We're gonna go numbers We're gonna add the decimal so we can see all those decimals gonna go to the home tab Font underline that and then we'll just multiply that out forty two two five five six nine times five point two oh six four and We get a number two large for the cell which happens to be 222 220,000 and Two cents next one says a company purchased equipment and signed a six year installment loan at ten percent annual interest the annual payments equal 5200 the present value of an annuity factor for six years At ten percent is four point three five five zero the present value of the loan is what so once again We have this even payments of five thousand two hundred easiest way to figure that out is to look at an annuity table and Look at the columns or and columns and rows intersecting between six years and ten percent And we're gonna get a number greater than one Because it's gonna be bigger because it's an annuity payment and we're gonna have an even number of these payments at five thousand two 200 for six years so again, you would think you'd multiply times six But it's gonna be less than six the factor because of course of the fact that there's ten percent of Interest or value in in here, so we're gonna stick the 5200 multiplied times the factor that just gave us the factor from the table being four point three five five I'm gonna go into the home tab numbers add decimals like that We're gonna go into the home tab font underline Multiply this out. We're gonna say the five thousand two hundred times the four point 355 gives us this 22646 and again that the instinct would be if there was no Interest factor here would be just to take this and say well if there's gonna be six years and there's six payments It should be five thousand two times six But that's not the present value because of the fact of this time value money or that this rate That we're gonna have for the present value, which is gonna be of course less than the actual dollar amount Next one says assets of thirty two million six twelve thousand total liabilities of nineteen million four sixty-two thousand and total equity of Thirteen million one hundred fifty thousand the debt to the debt to equity ratio for the period is what? So the debt to equity ratios is pretty easy to calculate it actually tells you exactly what it is It's debt over equity. It's a ratio. It's the debt compared to the equity So we're gonna say the debt then equals the liabilities of one nine four six two zero zero zero and the equity Equity is going to be this 13 one five zero zero zero zero and if we divide those out I'm gonna underline home tab font underline and we're gonna compare the debt The nineteen four sixty-two over divided by a ratio the equity 13150 and we come up not to one because we're gonna go to the home tab numbers add some decimals So notice the debt is greater than the equity remember what the equity represents assets minus liabilities equals equity it's kind of like the book value of the company and Therefore the debt is greater than than the equity in the company now note that we have three zeros here And if you wanted to round this since we're talking about millions of dollars, and it's probably okay to round it And it's even in terms of thousands So if you just plug in this into a calculator quickly It would be fine to say nineteen four six two over one three one five zero dividing each side By the thousand in this case dropping those zeros off because they're just zeros and we take the nineteen four six two divided by the thirteen one fifty and add Decimals and we would then get the same number