Question

Johnstone Company is facing several decisions regarding investing and financing activities. Address each decision independently. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) 1. On June 30, 2021, the Johnstone Company purchased equipment from Genovese Corp. Johnstone agreed to pay Genovese $24,000 on the purchase date and the balance in six annual installments of $7,000 on each June 30 beginning June 30, 2022. Assuming that an interest rate of 10% properly reflects the time value of money in this situation, at what amount should Johnstone value the equipment? 2. Johnstone needs to accumulate sufficient funds to pay a $540,000 debt that comes due on December 31, 2026. The company will accumulate the funds by making five equal annual deposits to an account paying 6% interest compounded annually. Determine the required annual deposit if the first deposit is made on December 31, 2021. 3. On January 1, 2021, Johnstone leased an office building. Terms of the lease require Johnstone to make 15 annual lease payments of $134,000 beginning on January 1, 2021. A 10% interest rate is implicit in the lease agreement. At what amount should Johnstone record the lease liability on January 1, 2021, before any lease payments are made?

Answer 1

(1) Value of the equipment on June 30, 2021 is the Amount of down payment + PV of Annuity of $7,000 for 6 years @10%

=$24,000+$30,486.82 = $54,486.82

Detailed calculation of PV of Annuity as follows:

с G в 1 Present Value of Annuity DEF Payments at the end of each period 3 Present value of annuity is calculated using the formula PVA=P*{[1-(1+r)^-n]/r]} 4 Where P= Periodical payments, 5 n= Number of payments. Eg. if number of years=N, then n=N*2 for semi annual payments 6 r= Rate of interest per period in decimals All amounts in $ Given that 9 Periodical payments (P)= 7000 No. of years (N)= 10 Rate of interest (% p.a)=R= 10 No. of payments a year (t)= 12 Calculations: Value 0.1 14 Interest rate per period in decimals (r )= 15 No. of periods (n)= 17 Formula R/(100*t) N*t (1+r)= (1+r)^-n= [1-(1+r)^-n]= [1-(1+r)^-n]/r= P*{[1-(1+r)^-n]/r]} Cell reference D10/(100*G10) G9*G10 1+G14 G164-G15 1-G17 G18/G14 D9*G19 Rounded to 1.1 0.56447393 0.43552607 4.355260699 30486.8249 $30,486.82 19 Pesent Value of Annuity Factor 20 Present value of annuity PV=

2. The amount required to be deposited every year is $90,371.75 calculated as follows:

G A B 1 Annuity Due Payment C D E Payments at the beginning of each period 3 Amount of periodical payments is calculated using the formula PMT=FV*[r/(1+r)^n-1]*[1/(1+r)] 4 Where PMT= Periodical payments required, 5 FV=Future value required 6 n= Number of payments. Eg. if number of years=N, then n=N*2 for semi annual payments 7 r= Rate of interest per period in decimals All amounts in $ Given that 10 Future value required FV= 540000 No. of years (N) 11 Rate of interest (% p.a)=R= 6 No. of payments a year(t) 12 Value 13 Calculations: 14 15 Interest rate per period in decimals (r)= 16 No. of periods (n)= 17 0.06 Nt Formula Cell reference R/(100*t) D11/(100*G11) G11*G11 (1+r)= 1+G15 (1+r)^n-1= G174G16 r/(1+r)^n-1 G15/G18 1/(1+r) 1/G17 FV*[r/(1+r)^n-1]*[1/(1+r)] 010*G19*G20 Rounded to 19 20 1.06 0.338225578 0.1773964 0.943396226 90371.75116 $90,371.75 21 Periodical payment required (PMT)= 22

(3) Value of the lease liability on January 1, 2021 before commencement of payments on the same day is the Present Value of Annuity Due of $134,000 for 15 years  @10%. Value ascertained is $1121136 calculated as follows:

1 Present Value of Annuity Due (advance) Payments at the beginning of of each period 3 Present value of annuity is calculated using the formula PVA=P+ P*{[1-(1+r)^-(n-1)]/r]} 4 Where P= Periodical payments, 5 n= Number of payments. 6 r= Rate of interest per period in decimals All amounts in $ Given that 134000 No. of years (N)= 10 Rate of interest (% p.a)=R= L 1 0 No. of payments a year (t) = 11 12 Calculations: 14 Interest rate per period in decimals (r)= 15 No. of periods (n)= 17 Formula Cell reference R/(100*t) D10/(100*G10) N*t G9*G10 (1+r)= 1+G14 (n-1)= (1+r)^-(n-1)= G164-G15 111- [1-(1+r)^-(n-1)]= 1-G17 [1-(1+r)^-(n-1)]/r= G18/614 P+P*{[1-(1+r)^-(n-1)]/r]} D9*G19 Rounded to Value 0.1 15 1.1 14 0.263331254 0.736668746 7.366687457 1121136.119 1121136 18 20 21 Present value of annuity PV= 23