Question

Solve each problem and show your work clearly

1. You plan to borrow $100,000 at 10%, compounded annually with payments at the end of each year. The length of the loan is 10 years. How big should your annual payments be?

2.A friend has asked for your help in determining whether she should invest in a property. She tells you that the property will have annual cash flows of $1,000 during the first two years and will increase by $200 every two years. She plans to keep the property for eight years and then sell it an expected price of $60,000. She has an annual discount rate of 8% and the current market price for the property is $50,000. Should your friend invest in this property? Calculate the NPV of this investment opportunity. Which should be the required discount rate to start investing in this property?

3. Patrick has recently been approved a mortgage for a property he was interested in investing for a while. The mortgage is for a thirty-year period with a 5% annual interest rate for a total amount of $90,000. These conditions result in an annual payment (debt service) of $5,855. What will be the interest and principal payments for the first four years of the mortgage? What will be the remaining principal balance at the end of the fourth year? (Show your calculations.)

4. You have an apartment for rent. One potential tenant has promised to sign an annual lease for eight years, with each year’s rent (paid at the end of the year) of $12,000. Rather than make annual payments, a second tenant has offered to pay you an upfront single cash payment for use of the apartment over the next eight years. If your discount rate is 5%, what is the minimum single cash payment that would make you sign the lease with the second tenant?

Answer 1

Gi Present value Auity = PMTX CATI) Y hese, 100, b00 Because have taker of annuity we P.V. t -oJ Loan at PMT annual dollar Paymentswhich is uiT ed tbe find out Y:10.1 PMT X OnI loo, 000PMT 6.1445613 - $16, 214. Sy 100, 000 annual Paymen fs .. 6.14567 $1000 a2 Cash flowsa Y = 200 Car 3nd year Sand 6 = $1490 yeaY 1 and 8 = $1600 at ar Price discaunt Yafe 81

Cash tlows dis Counted Calculafion of Present valve 995.9 dear cash flows Discount tachr 81 0-9259 1000 8S1. 3 0.8513 1000 952.56 O.1938 ఇం O.1350 1300 O.6806 1400 952.84 1400 o.6302 1600 O S835 933.6 1600 0 S403 864.48 60,000 0 S403 32 418 39,663.96 market Price = Current $ S0, 000 N.P.V 39,663.96 -s0, -10,331 04 It is at relemmended to InveStment is meg afive Simce N PV 0P

the The Yate where Yequired Yate alfo which Caled N.P.VE O Internal Yate Yeturn Can Cal lalated be RR and error sheet scientific method Spread Cal Cu lator this Comes Case app roa. 4-673-1 here 3) OUT Standing Prim di pal 90, 000 고mterest @s}. 90,000 S./ 4500 Anaual payment $5,655 pricipal ameunt paid annual padm ent Tnterest S8S5-M500 1355 reduction Princpal 9, o-1355 $86, 645 gear 2: Prin ci pay Dnterest=%% 645 S.J. $ T5,645 4432 25 Prind pal Paid= 5855- 413a.a5 1428.15 .Yeductionim primdpal88645-142a . 7s 81,282.25

ear 3 7rmcipat 81, 2aa 25 15 Interest 81, 222.asx s. 4361-11 Primcipal Pad -5ess -4361-1l 1493.89 Teduction Prindpal 5, 128.36 $IS Princi pal 85, 128.36 4286.42 8s,728.36*S Interest 58s5-4a56.42 Primapal Paid Is68 58 Prindpal 4,1isq. T8 .. 7educion of fourthar end at the Rabance 84,159.T8 Cash payment minimunm Simgle is Present Value t cash flows of $12 000 dis Counted at 5y ars PVIFA (Y-S. m for 6.4432 12 o00 6.46 32 $11, 5 S8.4