3. The table below provides cash flows for two mutually exclusive alternatives for developing a “Pay forRecreation" facility being considered by a county government in New Mexico. If money can be borrowed issuingbonds at the rate of 17% per year, using the rate of return analysis, find the attractive alternative between the twogiven proposals. For this question, use the interpolation between 10% and 20% of interest rates.YearAlt. AAlt. B-20M-40M1-204M7M21-403M3M41-002M4M

We will use Present Value approach to identify best alternative among given alternatives. Present Value of cash flow streams (a0,a1,...,an) for given interest rate "r" =a0/(1+r)+a1/(1+r)^2+...+an/(1+r)^nPresent Value of alternative A=-20M +4M(1/1.17+...+(1/1.17)^20) + 3M/(1.17)^20*(1/1.17+...+(1/1.17)^20) + 2M/(1.17)^40(1/(1-(1/1.17)) =-20M+4M*5.627767+3M/(1.17)^20*5.627767+2M/(1.17)^40*6.882353 =3.267533M Present Value of alternative B=-40M +7M(1/1.17+...+(1/1.17)^20) + 3M/(1.17)^20*(1/1.17+...+(1/1.17)^20) + 4M/(1.17)^40(1/(1-(1/1.17)) =-40M+7M*5.627767+3M/(1.17)^20*5.627767+4M/(1.17)^40*6.882353 =0.176637M We can clearly see that Present Value of alternative A > Present Value of alternative B Hence when r=17% the alternative A is the best choice Now lets find out for cost of capital between 10% to 20% and increasing it by 2% increment When r=10% PV of A = -20M +4M(1/1.1+...+(1/1.1)^20) + 3M/(1.1)^20*(1/1.1+...+(1/1.1)^20) + 2M/(1.1)^40(1/(1-(1/1.1))= $15.89M PV of B = -40M +7M(1/1.1+...+(1/1.1)^20) + 3M/(1.1)^20*(1/1.1+...+(1/1.1)^20) + 4M/(1.1)^40(1/(1-(1/1.1))=$20.27M When r=10% Alternative B to be chosen over Alternative A When r=12% PV of A = -20M +4M(1/1.12+...+(1/1.12)^20) + 3M/(1.12)^20*(1/1.12+...+(1/1.12)^20) + 2M/(1.12)^40(1/(1-(1/1.12))= $13.62M PV of B = -40M +7M(1/1.12+...+(1/1.12)^20) + 3M/(1.12)^20*(1/1.12+...+(1/1.12)^20) + 4M/(1.12)^40(1/(1-(1/1.12))=$15.69M When r=12% Alternative B to be chosen over Alternative A When r=14% PV of A = -20M +4M(1/1.14+...+(1/1.14)^20) + 3M/(1.14)^20*(1/1.14+...+(1/1.14)^20) + 2M/(1.14)^40(1/(1-(1/1.14))= $9.80M PV of B = -40M +7M(1/1.14+...+(1/1.14)^20) + 3M/(1.14)^20*(1/1.14+...+(1/1.14)^20) + 4M/(1.14)^40(1/(1-(1/1.14))=$9.39M When r=14% Alternative A to be chosen over Alternative B When r=16% PV of A = -20M +4M(1/1.16+...+(1/1.16)^20) + 3M/(1.16)^20*(1/1.16+...+(1/1.16)^20) + 2M/(1.16)^40(1/(1-(1/1.16))= $6.67M PV of B = -40M +7M(1/1.16+...+(1/1.16)^20) + 3M/(1.16)^20*(1/1.16+...+(1/1.16)^20) + 4M/(1.16)^40(1/(1-(1/1.16))=$4.22M When r=16% Alternative A to be chosen over Alternative B When r=18% PV of A = -20M +4M(1/1.18+...+(1/1.18)^20) + 3M/(1.18)^20*(1/1.18+...+(1/1.18)^20) + 2M/(1.18)^40(1/(1-(1/1.18))= $4.09M PV of B = -40M +7M(1/1.18+...+(1/1.18)^20 + 3M/(1.18)^20*(1/1.18+...+(1/1.18)^20) + 4M/(1.18)^40(1/(1-(1/1.18))=-$0.06M When r=18% Alternative A to be chosen over Alternative B Finally, When r=20% PV of A = -20M +4M(1/1.2+...+(1/1.2)^20) + 3M/(1.2)^20*(1/1.2+...+(1/1.2)^20) + 2M/(1.2)^40(1/(1-(1/1.2))= $1.91M PV of B = -40M +7M(1/1.2+...+(1/1.2)^20) + 3M/(1.2)^20*(1/1.2+...+(1/1.2)^20) + 4M/(1.2)^40(1/(1-(1/1.2))=-$3.67M When r=20% Alternative A to be chosen over Alternative B