On 1/1/2018, you deposit $20,000 into an account. At the end of each of the next

Question

On 1/1/2018, you deposit $20,000 into an account. At the end of each of the next four calendar quarters, the value of the account and the deposit/withdrawal activity is as follows: Date End Q1 End Q2 End Q3 Account Value $22,000 $23,000 26,000 Activity $2,000 withdrawal $7,000 deposit $8,000 withdrawal End Q4 21,000 The "account values" represent the amount in the account immediately before the deposit or withdrawal activity on that date. Find both the time-weighted rate of return and the dollar weighted rate of return on the account during 2015

Explanation / Answer

Time-weighted return Balance value Holding period return(Current qtr. End-previous qtr. End)/Prev.Qtr.end Initial Deposit 20000 End Qtr.1 20000 0.00% End Qtr.2 30000 50.00% End Qtr.3 14000 -53.33% End Qtr.4 21000 50.00% Now the time-weighted return= ((1+0%)*(1+0.50)*(1-0.5333)*(1+0.50))-1 5.01% Money-weighted Rate of Return Constructing the table for further deposits & withdrawals Beg. Balance Deposits Withdrawals Ending balance Net cash flow during the qtr. Changing signs ie. Initial Investment -20000 -20000 End Qtr.1 20000 4000 -2000 20000 2000 -2000 -2000 End Qtr.2 20000 10000 30000 10000 -10000 -10000 End Qtr.3 30000 4000 -8000 26000 -4000 4000 4000 End Qtr.4 26000 -5000 21000 -5000 5000 26000 21000 -2.01% Now calculating IRR with 20000 initial deposit as initial investment & cash outfolw,& treating all other deposits as investments & withdrawals as inflow to the investor, including the ending balance, 0=-20000+(-2000/(1+r)^1)+(-10000/(1+r)^2)+(4000/(1+r)^3)+(5000/(1+r)^4)+(21000/(1+r)^4)) IRR= -2.01% MWRR=-2.01% TWRR= 5.01%

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